Adaptation to gradual as compared with sudden visuo-motor distortions

Size: px
Start display at page:

Download "Adaptation to gradual as compared with sudden visuo-motor distortions"

Transcription

1 Exp Brain Res (1997) 115: Springer-Verlag 1997 RESEARCH NOTE selor&:florian A. Kagerer José L. Contreras-Vidal George E. Stelmach Adaptation to gradual as compared with sudden visuo-motor distortions csim&:received: 3 December 1996 / Accepted: 14 February p&:Abstract If visual feedback is discordant with movement direction, the visuo-motor mapping is disrupted, but can be updated with practice. In this experiment subjects practiced discrete arm movements under conditions of visual feedback rotation. One group was exposed to 10 -step increments of visual feedback rotation up to a total of 90, a second group to a 90 visual feedback rotation throughout the experiment. After the first group reached the 90 visual feedback rotation, its subjects performed faster, with less spatial error, and showed larger aftereffects than the subjects who practiced constantly under the 90 visual feedback rotation condition. Results suggest that gradually increasing feedback distortion allows more complete adaptation than a large, sudden distortion onset. dwk&:key words Visuomotor learning Internal models Visual feedback rotation Motor control&bdy: Introduction F. A. Kagerer J. L. Contreras-Vidal ( ) G. E. Stelmach Motor Control Laboratory, Arizona State University, Tempe, AZ , USA; Fax: +1 (602) , pepe@iris196.la.asu.edu&/fn-block: In visually guided limb movements a spatially perceived target direction is mapped into motor commands that drive the limb in the intended direction. This mapping between visual space and motor space is inappropriate if visual space is artificially rotated. In these circumstances movements become initially disordered with erratic movement paths. For example, a 90 rotation of visual space requires a movement direction that is perpendicular to the movement direction necessary when visual space and movement space are compatible. This results in a deviation of the movement path from a straight line. The movement initially starts in the direction of the visually perceived target, but as the lack of correspondence between visual feedback and performed movement becomes evident and the subject begins to update the visuo-motor mapping, corrections in the movement are made (Cunningham 1989). With practice, the initially erratic movement paths evolve as spirals and semicircles, and eventually appear as straight lines to the targets (Cunningham and Vardi 1990; Roby-Brami and Burnod 1995). The estimation of a rotational bias during a previous trial appears to induce an update of a correction factor at the sensory-motor map that is retained at the onset of the next trial. This adaptive process is based on the updating of the mapping between internal visual and motor representations of space which takes place over time, a process which is not easily overridden by conscious effort (Cunningham and Welch 1994). Previous studies involving visual-motor adaptation have been primarily concerned with the spatial properties of aiming movements during adaptation to changed execution conditions (Cunningham 1989; Bock 1992; Bock et al. 1992) rather than examining adaptation as a function of the time course of the perturbation. If the relative difficulty, e.g., measured by spatial error or movement time, of different transformations is preserved, i.e., if error patterns are invariant for adaptation to different degrees of perturbation, then the transformation-related error patterns may be attributed to structural (time-invariant) rather than dynamical (time-varying) properties of the system (Shadmer and Mussa-Ivaldi 1994). Our question is how a gradual increase in visual feedback rotation from 0 to 90 affects the adaptation of the visuo-motor map (a type of internal model), compared with a sudden rotation of 90. Recent experiments suggest that the central nervous system (CNS) uses sensory feedback to update an internal model of the interaction of the limb and the environment (Roby-Brami and Burnod 1995). As the CNS adapts to a new condition, the emphasis of the control strategy shifts from feedback toward feedforward control; as a result there is less need for on-line corrections. For example, in rotated visual feedback tasks, movement performance improvement correlates with a decrease of the initial directional error appearing immediately after movement onset, when visual feedback is not yet available. We hypothesized that gradual changes

2 558 in visual feedback rotation allow the system to estimate small rotational movement corrections that require only small updates in the visuo-motor map based on previously learned information (e.g., acquired before the rotation of visual feedback), while sudden large changes in feedback rotation initially require a search in visuo-motor space to minimize the error of performance with respect to the desired internal model parameters. According to this hypothesis it is predicted that a gradually increasing distortion of visual feedback would allow a better updating of the internal model than a sudden 90 distortion. We also expected larger aftereffects (movement paths mirroring the deviations found during practice) for the former, when the visual feedback rotation was suddenly removed after adaptation. Materials and methods Subjects Ten right-handed, young college students, who were randomly assigned to two groups of five subjects were tested. All subjects signed informed consent statements. Apparatus For data collection a Calcomp 9100 Series digitizing tablet (sampling rate 100 Hz) was used. Stimuli were presented on a computer screen [21 inch (53.5 cm), SVGA with points]. The targets were randomly presented in one of four different locations, around the home position in the center (see Fig. 2). Home position and target were visible over the whole duration of the trial. Experimental design Subjects made horizontal arm movements with a pen in their right hand on the digitizing tablet to the four different target directions that appeared one at a time on a computer screen in front of them (Fig. 2A); they had no vision of their moving arm and hand. Under a condition where visual feedback was rotated 90 counterclockwise, a movement away from the body towards the left on the horizontal tablet produced a downward left movement of the cursor on the vertical screen; analogous to that, a 10 rotation required a smaller change of movement direction relative to the cursor movement displayed.&fn.1:1 Subjects were instructed to make straight paths to the targets as fast as possible. Immediate feedback about movement time was given after each trial (Kagerer et al. 1995). To start each trial subjects had to click the pen briefly in the home position, wait for an acoustic stimulus appearing after a random delay of between 200 and 2000 ms, and start the movement from a home position toward the target upon appearance of the acoustic stimulus. An experimental session consisted of 11 blocks: one initial block of 40 movements aimed to four targets located at 45, 135, 225 and 335 (10 movements per target direction) as baseline condition (normal visual feedback), and 10 blocks of 60 move- 1 It should be noted that this arrangement required a second transformation besides the visual feedback rotation, namely a transformation from the horizontal plane of the movements to the vertical plane of the visual feedback. This second transformation was considered to have negligible influence on the subjects performance since all of them were used to working with a computer mouse, where the same transformation has to be made. Moreover, the same setup was used for both groups.&/fn: ments (15 per target direction) as practice condition (rotated visual feedback). Following adaptation, 16 movements (four per target direction) were administered under baseline conditions to test for aftereffects; two subjects in each group performed only four movements (one per target direction). The order of appearance of the four target locations was randomized within each block, but each target appeared the same number of times. One group was presented with a 90 visual feedback rotation from the first block of practice onward (S: sudden onset group), whereas a second group was presented with a blockwise, monotonic increase in rotation of visual feedback by 10 increments, until the rotation had reached 90 (G: gradual onset group). This block, containing the largest and most difficult visual feedback distortion, was administered twice. Both groups performed the same number of trials. Data acquisition Movement trajectories were recorded by sampling the position of a pen subjects held in their right hand; a cursor on the screen moving with unitary gain relative to the pen movements provided the visual feedback. Recording began with the acoustic start signal and ended with the second acoustic signal upon arriving at the target. Movement time (MT) was calculated as the difference in time between leaving the home position and entering the target. Straightness of the movements was measured by calculating the root mean squared error (RMSE), defined as RMSE = where (x a, y a ) are points of the actual trajectory, (x i, y i ) the corresponding points on an ideal, straight line between home position and target, and N is the number of samples (Cunningham 1989). The initial directional error (IDE) was measured as the angular directional difference between movement path and an ideal straight line between home position and target; IDE was assessed during the first 80 ms of movement to make sure that no visual feedback signals could be utilized. Data analysis The collected data were filtered off-line with a 10 Hz lowpass filter, and RMSE, MT and IDE were calculated. For analysis, the movements toward the four target locations belonging to the same trial were pooled and one mean was calculated, resulting in 164 data points per subject (Fig. 1A). A Group Trials repeated-measures ANOVA was performed for RMSE, MT and IDE for the last two practice blocks. Since only four observations were taken into account, aftereffects were analyzed using the t-test. Results L NM 2 2 ( xa xi) + ya yi N a During the baseline condition there was no statistically significant difference between the groups. Repeatedmeasures ANOVA (Groups Trials) showed no significant group differences for RMSE, MT and IDE (P>0.05). As expected, in the practice condition the two groups showed rather different performance curves. The sudden onset condition resulted in a severe disruption of the straightness of movements, as shown by the larger RMSE at the beginning of practice (Fig. 1A, see also Fig. 2A C for the movement paths), decreasing exponentially with practice and approaching a baseline level; MT and IDE also decreased in a similar way with practice. f O QP 05.

3 559 Fig. 1A D Performance curves of the two groups. A The minimal disruption of performance, as measured by spatial error, under conditions of gradually increasing distortion of visual space (group G: thin line), and the consistently larger root mean square error (RMSE) resulting from the sudden onset of the distortion (group S: bold line). The characteristics of this performance curve were also present in the curves for initial directional error (IDE) and movement time (MT) (not shown). The first ten trials show the baseline performance. Each of the longer ticks on the x-axis marks the beginning of a block, which meant an increase by 10 for group G, while group S was always presented with the same visual feedback rotation of 90. The empty arrows at the right side of the graph mark the aftereffect, which was less pronounced in group S than in group G. B The last 120 practice movements (pooled to the 30 trials shown), where both groups were exposed to the 90 feedback rotation. C,D The groups performance for IDE and MT for the last two blocks of practice&/f :c.gi The gradual onset condition caused little disruption of the subjects performance over the whole range of distortions (Figs. 1A, 2B,C). Linear regression showed a significant correlation between increasing RMSE and trial number, indicating the increasing difficulty of the transformation (r=0.66, slope=0.02, P<0.01). Within blocks, in group G only the first two trials of each block showed a slight increase in RMSE, the values thereafter dropping immediately to baseline level. Although the performance curves for group S approach those for group G, the two groups show clear differences in performance at the 90 rotation condition (last two shaded blocks in Fig. 1B). Subjects in group G performed better than subjects in group S (who at that point had practiced the 90 rotation for 480 trials) in terms of RMSE, MT and IDE. A repeated-measures ANOVA (Groups Trials) showed that in the last block, when the visual feedback rotation was identical for the two groups, group G showed a significantly smaller RMSE (F 1,8 =7.03, P<0.05) than group S (Fig. 1B). A linear fit showed a significant negative correlation between RMSE and trial number over the last two blocks (r= 0.56, slope= 0.08, P<0.001) for group G, which suggests a further reduction of RMSE during the final trials. Group S, on the other hand, showed a higher RMSE, and a linear fit revealed no tendency for further improvement (r=0.03, slope= 0.005, P>0.05), suggesting that the subjects did not update their internal model during the last 120 movements. Another indicator of the adaptation is the IDE, measured 80 ms after movement onset. If a movement starts in the deviant direction, its RMSE is likely to be larger, assuming that subjects use the strategy of moving in a curved path rather than using a straight path correction. Repeated-measures ANOVA showed that in the last two blocks there was a significant main effect for group (F 1, 8 =7.11, P<0.05), indicating that the IDE of group G was significantly smaller than the IDE of group S. A linear fit showed a significant negative correlation between IDE and trials (r= 0.6, slope= 0.2, P<0.001) and no correlation for group S (r=0.03, slope=0.06, P>0.05). As Fig. 1C illustrates, in the last block IDE of group G is closer to the desired value of zero than that of group S (mean values of 6.4 vs 13.45, respectively). Our results showed that IDE correlated very well with RMSE (group G: r=0.83, P<0.001; group S: r=0.93, P<0.001). We found a similar trend for MT during the last two blocks. Since aftereffects are usually very transient and dissipate quickly, we compared RMSE and IDE only for the first four post-practice movements (baseline condition) for each group. The movement paths of one subject for each group, depicted in Fig. 2D, represent the group results very well. Both groups showed an aftereffect and moved initially in the direction of the rotated feedback. However, t-tests revealed that RMSE and IDE for group G during post-practice performance under normal visual feedback were significantly higher than those for group

4 :b.lbt/& 560 Table 1 Aftereffect: Mean root mean square error (RMSE), initial directional error (IDE) and standard deviations for the first four trials under normal visual feedback condition after adaptation. With one exception, the subjects of the sudden onset group (S) show a smaller RMSE than those of the gradual onset group (G). Subjects 2 and 3 of each group performed only one trial, therefore there is no standard deviation. Positive IDE values denote clockwise, negative values counterclockwise deviation from a straight line to the target&/tbl.c:&tbl.b: Gradual onset group (G) Sudden onset group (S) Subjects RMSE [mm] IDE (deg) RMSE [mm] IDE (deg) (2.8) 55.3 (4.6) 20.4 (0.9) 49.2 (3.2) (8.4) 30.6 (14.8) 18.7 (9.4) 33.4 (19.1) (1.6) 43.0 (5.9) 6.1 (2.3) 1.3 (5.4) Fig. 2A D Movement paths of one subject of each group; the first four trials of a block are shown. A Home position (HP) and targets (T) are displayed. Subjects started from the home position, moving to the target (1 1 cm) displayed on the monitor. Left-hand column: A baseline performance, B performance under 10 visual feedback rotation and C performance under 90 visual feedback rotation (last but one block, which was the first block with 90 rotation for group G). Variability is small, and the curvature under the 90 condition is just slightly higher than during baseline performance. Right-hand column: A baseline performance, B performance under 90 visual feedback rotation (first practice block) and C 90 visual feedback rotation (last but one block). D Aftereffects are more pronounced after gradual than after sudden onset practice, suggesting a more elaborated visuo-motor map for group G&/f :c.gi S (RMSE: t=7.43, P<0.001; IDE: t=6.15, P<0.001) (Table 1). Discussion The results suggest that the smaller RMSE and IDE, as well as the shorter MT, for group G may result from a more elaborated updating of the visuo-motor map due to exposure to a slowly increasing visual feedback rotation. Our results on the aftereffects are in agreement with this view. The aftereffect can be seen as an indicator of the degree to which the internal model has been updated during adaptation. The first few post-practice trials under normal visual feedback condition are performed under the previously adapted visuo-motor map. Therefore, a more elaborated visuo-motor map would cause a larger RMSE and IDE, and longer MT. Since at late stages of adaptation the movement path usually takes the form of a shallow arc (Fig. 2D, sudden condition), and since this kind of movement usually shows only a little variability in the tangential velocity, it can be assumed that a slightly curved line can be executed as fast as a straight line. Therefore, straightness of a path measured as RMSE with reference to baseline performance provides information about the degree to which the subject s internal model has adapted to the rotated feedback. IDE may be considered as an indicator for the visuo-motor transformations in the initial phase of the movement, as feedback is not likely to have an influence then. These results suggest that gradually increasing visual feedback rotation allows a more complete adaptation to this distortion, with minimal disruption in performance, compared with a sudden large distortion onset. Since the increase in the distortion was stepwise, one could argue that subjects anticipated a change with every new block. The increase in RMSE at the beginning of each block, however, does not support this argument. Also, at the end of the experiment all subjects in group G reported that they did not notice any systematic change during practice, except during the aftereffect trials. These findings may represent a generalized feature of adaptation mechanisms that may be applicable to other conditions which require adaptation to new environments. We have presented evidence that the application of a distortion that evolves gradually to its desired final level results in minimal degradation of performance compared with a single large distortion, and in a more elaborated sensorimotor mapping, as shown by the larger aftereffects. 2.p&:Acknowledgements This research was supported by a Flinn Foundation Grant in the Computational Aspects of Motor Adaptation. We thank our colleagues at the Motor Control Laboratory at ASU for their comments on a earlier draft of this manuscript.

5 561 References Bock O (1992) Adaptation of aimed arm movements to sensorimotor discordance: evidence for direction-independent gain control. Behav Brain Res 51: Bock O, Howard IP, Money KE, Arnold KE (1992) Accuracy of aimed arm movements in changed gravity. Aviat Space Environ Med 63: Cunningham HA (1989) Aiming error under transformed spatial mappings suggests a structure for visual-motor maps. J Exp Psychol Hum Percept Perform 15: Cunningham HA, Vardi I (1990) A vector-sum process produces curved aiming paths under rotated visual-motor mappings. Biol Cybern 64: Cunningham HA, Welch RB (1994) Multiple concurrent visualmotor mappings: implications for models of adaptation. J Exp Psychol Hum Percept Perform 20: Kagerer F, Bloedel JR, Stelmach GE (1995) Learning of visuomotor coordination with rotated visual feedback. Soc Neurosci Abstr 21: 1443 Roby-Brami A, Burnod Y (1995) Learning a new visuomotor transformation: error correction and generalization. Cogn Brain Res 2: Shadmer R, Mussa-Ivaldi RA (1994) Adaptive representation of dynamics during learning a motor task. J Neurosci 14:

FREE FALL. Introduction. Reference Young and Freedman, University Physics, 12 th Edition: Chapter 2, section 2.5

FREE FALL. Introduction. Reference Young and Freedman, University Physics, 12 th Edition: Chapter 2, section 2.5 Physics 161 FREE FALL Introduction This experiment is designed to study the motion of an object that is accelerated by the force of gravity. It also serves as an introduction to the data analysis capabilities

More information

Reflection and Refraction

Reflection and Refraction Equipment Reflection and Refraction Acrylic block set, plane-concave-convex universal mirror, cork board, cork board stand, pins, flashlight, protractor, ruler, mirror worksheet, rectangular block worksheet,

More information

Reduction of the flash-lag effect in terms of active observation

Reduction of the flash-lag effect in terms of active observation Attention, Perception, & Psychophysics 2010, 72 (4), 1032-1044 doi:10.3758/app.72.4.1032 Reduction of the flash-lag effect in terms of active observation MAKOTO ICHIKAWA Chiba University, Chiba, Japan

More information

Effects of Orientation Disparity Between Haptic and Graphic Displays of Objects in Virtual Environments

Effects of Orientation Disparity Between Haptic and Graphic Displays of Objects in Virtual Environments Human Computer Interaction INTERACT 99 Angela Sasse and Chris Johnson (Editors) Published by IOS Press, c IFIP TC.13, 1999 1 Effects of Orientation Disparity Between Haptic and Graphic Displays of Objects

More information

FORCE ON A CURRENT IN A MAGNETIC FIELD

FORCE ON A CURRENT IN A MAGNETIC FIELD 7/16 Force current 1/8 FORCE ON A CURRENT IN A MAGNETIC FIELD PURPOSE: To study the force exerted on an electric current by a magnetic field. BACKGROUND: When an electric charge moves with a velocity v

More information

Representing Vector Fields Using Field Line Diagrams

Representing Vector Fields Using Field Line Diagrams Minds On Physics Activity FFá2 5 Representing Vector Fields Using Field Line Diagrams Purpose and Expected Outcome One way of representing vector fields is using arrows to indicate the strength and direction

More information

Cabri Geometry Application User Guide

Cabri Geometry Application User Guide Cabri Geometry Application User Guide Preview of Geometry... 2 Learning the Basics... 3 Managing File Operations... 12 Setting Application Preferences... 14 Selecting and Moving Objects... 17 Deleting

More information

ε: Voltage output of Signal Generator (also called the Source voltage or Applied

ε: Voltage output of Signal Generator (also called the Source voltage or Applied Experiment #10: LR & RC Circuits Frequency Response EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor graph paper (optional) (3) Patch Cords Decade resistor, capacitor, and

More information

GENERAL SCIENCE LABORATORY 1110L Lab Experiment 6: Ohm s Law

GENERAL SCIENCE LABORATORY 1110L Lab Experiment 6: Ohm s Law GENERAL SCIENCE LABORATORY 1110L Lab Experiment 6: Ohm s Law OBJECTIVES: To verify Ohm s law, the mathematical relationship among current, voltage or potential difference, and resistance, in a simple circuit.

More information

Self Organizing Maps: Fundamentals

Self Organizing Maps: Fundamentals Self Organizing Maps: Fundamentals Introduction to Neural Networks : Lecture 16 John A. Bullinaria, 2004 1. What is a Self Organizing Map? 2. Topographic Maps 3. Setting up a Self Organizing Map 4. Kohonen

More information

CALCULATIONS & STATISTICS

CALCULATIONS & STATISTICS CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents

More information

1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D

1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D Chapter 28: MAGNETIC FIELDS 1 Units of a magnetic field might be: A C m/s B C s/m C C/kg D kg/c s E N/C m 2 In the formula F = q v B: A F must be perpendicular to v but not necessarily to B B F must be

More information

Acceleration Introduction: Objectives: Methods:

Acceleration Introduction: Objectives: Methods: Acceleration Introduction: Acceleration is defined as the rate of change of velocity with respect to time, thus the concepts of velocity also apply to acceleration. In the velocity-time graph, acceleration

More information

Linear Motion vs. Rotational Motion

Linear Motion vs. Rotational Motion Linear Motion vs. Rotational Motion Linear motion involves an object moving from one point to another in a straight line. Rotational motion involves an object rotating about an axis. Examples include a

More information

Chapter 3 Falling Objects and Projectile Motion

Chapter 3 Falling Objects and Projectile Motion Chapter 3 Falling Objects and Projectile Motion Gravity influences motion in a particular way. How does a dropped object behave?!does the object accelerate, or is the speed constant?!do two objects behave

More information

Physics 41, Winter 1998 Lab 1 - The Current Balance. Theory

Physics 41, Winter 1998 Lab 1 - The Current Balance. Theory Physics 41, Winter 1998 Lab 1 - The Current Balance Theory Consider a point at a perpendicular distance d from a long straight wire carrying a current I as shown in figure 1. If the wire is very long compared

More information

Measurement of Charge-to-Mass (e/m) Ratio for the Electron

Measurement of Charge-to-Mass (e/m) Ratio for the Electron Measurement of Charge-to-Mass (e/m) Ratio for the Electron Experiment objectives: measure the ratio of the electron charge-to-mass ratio e/m by studying the electron trajectories in a uniform magnetic

More information

ART 269 3D Animation Fundamental Animation Principles and Procedures in Cinema 4D

ART 269 3D Animation Fundamental Animation Principles and Procedures in Cinema 4D ART 269 3D Animation Fundamental Animation Principles and Procedures in Cinema 4D Components Tracks An animation track is a recording of a particular type of animation; for example, rotation. Some tracks

More information

ASSIGNMENT 4 PREDICTIVE MODELING AND GAINS CHARTS

ASSIGNMENT 4 PREDICTIVE MODELING AND GAINS CHARTS DATABASE MARKETING Fall 2015, max 24 credits Dead line 15.10. ASSIGNMENT 4 PREDICTIVE MODELING AND GAINS CHARTS PART A Gains chart with excel Prepare a gains chart from the data in \\work\courses\e\27\e20100\ass4b.xls.

More information

LAB 6 - GRAVITATIONAL AND PASSIVE FORCES

LAB 6 - GRAVITATIONAL AND PASSIVE FORCES L06-1 Name Date Partners LAB 6 - GRAVITATIONAL AND PASSIVE FORCES OBJECTIVES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies

More information

A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion

A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion Objective In the experiment you will determine the cart acceleration, a, and the friction force, f, experimentally for

More information

Pressure in Fluids. Introduction

Pressure in Fluids. Introduction Pressure in Fluids Introduction In this laboratory we begin to study another important physical quantity associated with fluids: pressure. For the time being we will concentrate on static pressure: pressure

More information

Visual-based ID Verification by Signature Tracking

Visual-based ID Verification by Signature Tracking Visual-based ID Verification by Signature Tracking Mario E. Munich and Pietro Perona California Institute of Technology www.vision.caltech.edu/mariomu Outline Biometric ID Visual Signature Acquisition

More information

Managerial Economics Prof. Trupti Mishra S.J.M. School of Management Indian Institute of Technology, Bombay. Lecture - 13 Consumer Behaviour (Contd )

Managerial Economics Prof. Trupti Mishra S.J.M. School of Management Indian Institute of Technology, Bombay. Lecture - 13 Consumer Behaviour (Contd ) (Refer Slide Time: 00:28) Managerial Economics Prof. Trupti Mishra S.J.M. School of Management Indian Institute of Technology, Bombay Lecture - 13 Consumer Behaviour (Contd ) We will continue our discussion

More information

Research question: How does the velocity of the balloon depend on how much air is pumped into the balloon?

Research question: How does the velocity of the balloon depend on how much air is pumped into the balloon? Katie Chang 3A For this balloon rocket experiment, we learned how to plan a controlled experiment that also deepened our understanding of the concepts of acceleration and force on an object. My partner

More information

AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false?

AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The

More information

Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name

Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name Name If you think that no correct answer is provided, give your answer, state your reasoning briefly; append additional sheet of paper if necessary. 1. A particle (q = 5.0 nc, m = 3.0 µg) moves in a region

More information

LAB 6: GRAVITATIONAL AND PASSIVE FORCES

LAB 6: GRAVITATIONAL AND PASSIVE FORCES 55 Name Date Partners LAB 6: GRAVITATIONAL AND PASSIVE FORCES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the attraction

More information

Skill acquisition. Skill acquisition: Closed loop theory Feedback guides learning a motor skill. Problems. Motor learning practice

Skill acquisition. Skill acquisition: Closed loop theory Feedback guides learning a motor skill. Problems. Motor learning practice Motor learning theories closed loop theory schema theory hierarchical theory Skill acquisition Motor learning practice Fitt s three stages motor imagery physical changes Skill acquisition: Closed loop

More information

Summary of important mathematical operations and formulas (from first tutorial):

Summary of important mathematical operations and formulas (from first tutorial): EXCEL Intermediate Tutorial Summary of important mathematical operations and formulas (from first tutorial): Operation Key Addition + Subtraction - Multiplication * Division / Exponential ^ To enter a

More information

Sensory-motor control scheme based on Kohonen Maps and AVITE model

Sensory-motor control scheme based on Kohonen Maps and AVITE model Sensory-motor control scheme based on Kohonen Maps and AVITE model Juan L. Pedreño-Molina, Antonio Guerrero-González, Oscar A. Florez-Giraldo, J. Molina-Vilaplana Technical University of Cartagena Department

More information

Chapter 10. Key Ideas Correlation, Correlation Coefficient (r),

Chapter 10. Key Ideas Correlation, Correlation Coefficient (r), Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables

More information

Laboratory Report Scoring and Cover Sheet

Laboratory Report Scoring and Cover Sheet Laboratory Report Scoring and Cover Sheet Title of Lab _Newton s Laws Course and Lab Section Number: PHY 1103-100 Date _23 Sept 2014 Principle Investigator _Thomas Edison Co-Investigator _Nikola Tesla

More information

Lab 1: Introduction to PSpice

Lab 1: Introduction to PSpice Lab 1: Introduction to PSpice Objectives A primary purpose of this lab is for you to become familiar with the use of PSpice and to learn to use it to assist you in the analysis of circuits. The software

More information

The DC Motor. Physics 1051 Laboratory #5 The DC Motor

The DC Motor. Physics 1051 Laboratory #5 The DC Motor The DC Motor Physics 1051 Laboratory #5 The DC Motor Contents Part I: Objective Part II: Introduction Magnetic Force Right Hand Rule Force on a Loop Magnetic Dipole Moment Torque Part II: Predictions Force

More information

Spring Force Constant Determination as a Learning Tool for Graphing and Modeling

Spring Force Constant Determination as a Learning Tool for Graphing and Modeling NCSU PHYSICS 205 SECTION 11 LAB II 9 FEBRUARY 2002 Spring Force Constant Determination as a Learning Tool for Graphing and Modeling Newton, I. 1*, Galilei, G. 1, & Einstein, A. 1 (1. PY205_011 Group 4C;

More information

1 One Dimensional Horizontal Motion Position vs. time Velocity vs. time

1 One Dimensional Horizontal Motion Position vs. time Velocity vs. time PHY132 Experiment 1 One Dimensional Horizontal Motion Position vs. time Velocity vs. time One of the most effective methods of describing motion is to plot graphs of distance, velocity, and acceleration

More information

Unit 4 Practice Test: Rotational Motion

Unit 4 Practice Test: Rotational Motion Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle

More information

PENDULUM PERIODS. First Last. Partners: student1, student2, and student3

PENDULUM PERIODS. First Last. Partners: student1, student2, and student3 PENDULUM PERIODS First Last Partners: student1, student2, and student3 Governor s School for Science and Technology 520 Butler Farm Road, Hampton, VA 23666 April 13, 2011 ABSTRACT The effect of amplitude,

More information

Experiment 8: Undriven & Driven RLC Circuits

Experiment 8: Undriven & Driven RLC Circuits Experiment 8: Undriven & Driven RLC Circuits Answer these questions on a separate sheet of paper and turn them in before the lab 1. RLC Circuits Consider the circuit at left, consisting of an AC function

More information

Subjects. Subjects were undergraduates at the University of California, Santa Barbara, with

Subjects. Subjects were undergraduates at the University of California, Santa Barbara, with Category-specific visual attention 1 SI Appendix 1 Method Subjects. Subjects were undergraduates at the University of California, Santa Barbara, with normal or corrected-to-normal vision. Exp 1: n=30;

More information

Solving Simultaneous Equations and Matrices

Solving Simultaneous Equations and Matrices Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering

More information

User Eye Fatigue Detection via Eye Movement Behavior

User Eye Fatigue Detection via Eye Movement Behavior This is a pre-print User Eye Fatigue Detection via Eye Movement Behavior Evgeniy Abdulin Department of Computer Science Texas State University San Marcos, TX 78666 e_a146@txstate.edu Oleg Komogortsev Department

More information

AP Physics 1 and 2 Lab Investigations

AP Physics 1 and 2 Lab Investigations AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks

More information

Experiment #1, Analyze Data using Excel, Calculator and Graphs.

Experiment #1, Analyze Data using Excel, Calculator and Graphs. Physics 182 - Fall 2014 - Experiment #1 1 Experiment #1, Analyze Data using Excel, Calculator and Graphs. 1 Purpose (5 Points, Including Title. Points apply to your lab report.) Before we start measuring

More information

Torque and Rotary Motion

Torque and Rotary Motion Torque and Rotary Motion Name Partner Introduction Motion in a circle is a straight-forward extension of linear motion. According to the textbook, all you have to do is replace displacement, velocity,

More information

FRICTION, WORK, AND THE INCLINED PLANE

FRICTION, WORK, AND THE INCLINED PLANE FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle

More information

DRAFTING MANUAL. Gears (Bevel and Hypoid) Drafting Practice

DRAFTING MANUAL. Gears (Bevel and Hypoid) Drafting Practice Page 1 1.0 General This section provides the basis for uniformity in engineering gears drawings and their technical data for gears with intersecting axes (bevel gears), and nonparallel, nonintersecting

More information

Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6. Instructions: 1. In the formula F = qvxb:

Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6. Instructions: 1. In the formula F = qvxb: Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6 Signature Name (Print): 4 Digit ID: Section: Instructions: Answer all questions 24 multiple choice questions. You may need to do some calculation.

More information

Correcting the Lateral Response Artifact in Radiochromic Film Images from Flatbed Scanners

Correcting the Lateral Response Artifact in Radiochromic Film Images from Flatbed Scanners Correcting the Lateral Response Artifact in Radiochromic Film Images from Flatbed Scanners Background The lateral response artifact (LRA) in radiochromic film images from flatbed scanners was first pointed

More information

EXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives

EXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives EXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives to verify how the distance of a freely-falling body varies with time to investigate whether the velocity

More information

Harmonic oscillations of spiral springs Springs linked in parallel and in series

Harmonic oscillations of spiral springs Springs linked in parallel and in series .3.26 Related topics Spring constant, Hooke s Law, oscillations, limit of elasticity, parallel springs, serial springs, use of an interface. Principle and task The spring constant D is determined for different

More information

AP1 Waves. (A) frequency (B) wavelength (C) speed (D) intensity. Answer: (A) and (D) frequency and intensity.

AP1 Waves. (A) frequency (B) wavelength (C) speed (D) intensity. Answer: (A) and (D) frequency and intensity. 1. A fire truck is moving at a fairly high speed, with its siren emitting sound at a specific pitch. As the fire truck recedes from you which of the following characteristics of the sound wave from the

More information

Railway Track Design

Railway Track Design Chapter Railway Track Design Basic considerations and guidelines to be used in the establishment of railway horizontal and vertical alignments. The route upon which a train travels and the track is constructed

More information

Refraction of Light at a Plane Surface. Object: To study the refraction of light from water into air, at a plane surface.

Refraction of Light at a Plane Surface. Object: To study the refraction of light from water into air, at a plane surface. Refraction of Light at a Plane Surface Object: To study the refraction of light from water into air, at a plane surface. Apparatus: Refraction tank, 6.3 V power supply. Theory: The travel of light waves

More information

Newton s Second Law. ΣF = m a. (1) In this equation, ΣF is the sum of the forces acting on an object, m is the mass of

Newton s Second Law. ΣF = m a. (1) In this equation, ΣF is the sum of the forces acting on an object, m is the mass of Newton s Second Law Objective The Newton s Second Law experiment provides the student a hands on demonstration of forces in motion. A formulated analysis of forces acting on a dynamics cart will be developed

More information

Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data

Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data Introduction In several upcoming labs, a primary goal will be to determine the mathematical relationship between two variable

More information

Lesson 1: Positive and Negative Numbers on the Number Line Opposite Direction and Value

Lesson 1: Positive and Negative Numbers on the Number Line Opposite Direction and Value Positive and Negative Numbers on the Number Line Opposite Direction and Value Student Outcomes Students extend their understanding of the number line, which includes zero and numbers to the right or above

More information

Magnetic Fields and Their Effects

Magnetic Fields and Their Effects Name Date Time to Complete h m Partner Course/ Section / Grade Magnetic Fields and Their Effects This experiment is intended to give you some hands-on experience with the effects of, and in some cases

More information

How far ahead do we look when required to step on specific locations in the travel path during locomotion?

How far ahead do we look when required to step on specific locations in the travel path during locomotion? Exp Brain Res (2003) 148:133 138 DOI 10.1007/s00221-002-1246-y RESEARCH NOTE Aftab E. Patla Joan N. Vickers How far ahead do we look when required to step on specific locations in the travel path during

More information

ENERGYand WORK (PART I and II) 9-MAC

ENERGYand WORK (PART I and II) 9-MAC ENERGYand WORK (PART I and II) 9-MAC Purpose: To understand work, potential energy, & kinetic energy. To understand conservation of energy and how energy is converted from one form to the other. Apparatus:

More information

Determination of Acceleration due to Gravity

Determination of Acceleration due to Gravity Experiment 2 24 Kuwait University Physics 105 Physics Department Determination of Acceleration due to Gravity Introduction In this experiment the acceleration due to gravity (g) is determined using two

More information

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

More information

Calculator Notes for the TI-Nspire and TI-Nspire CAS

Calculator Notes for the TI-Nspire and TI-Nspire CAS CHAPTER 11 Calculator Notes for the Note 11A: Entering e In any application, press u to display the value e. Press. after you press u to display the value of e without an exponent. Note 11B: Normal Graphs

More information

Video-Based Eye Tracking

Video-Based Eye Tracking Video-Based Eye Tracking Our Experience with Advanced Stimuli Design for Eye Tracking Software A. RUFA, a G.L. MARIOTTINI, b D. PRATTICHIZZO, b D. ALESSANDRINI, b A. VICINO, b AND A. FEDERICO a a Department

More information

The Bullet-Block Mystery

The Bullet-Block Mystery LivePhoto IVV Physics Activity 1 Name: Date: 1. Introduction The Bullet-Block Mystery Suppose a vertically mounted 22 Gauge rifle fires a bullet upwards into a block of wood (shown in Fig. 1a). If the

More information

Centripetal Force. This result is independent of the size of r. A full circle has 2π rad, and 360 deg = 2π rad.

Centripetal Force. This result is independent of the size of r. A full circle has 2π rad, and 360 deg = 2π rad. Centripetal Force 1 Introduction In classical mechanics, the dynamics of a point particle are described by Newton s 2nd law, F = m a, where F is the net force, m is the mass, and a is the acceleration.

More information

Fixplot Instruction Manual. (data plotting program)

Fixplot Instruction Manual. (data plotting program) Fixplot Instruction Manual (data plotting program) MANUAL VERSION2 2004 1 1. Introduction The Fixplot program is a component program of Eyenal that allows the user to plot eye position data collected with

More information

Equations of Lines and Planes

Equations of Lines and Planes Calculus 3 Lia Vas Equations of Lines and Planes Planes. A plane is uniquely determined by a point in it and a vector perpendicular to it. An equation of the plane passing the point (x 0, y 0, z 0 ) perpendicular

More information

PERSPECTIVE. How Top-Down is Visual Perception?

PERSPECTIVE. How Top-Down is Visual Perception? PERSPECTIVE How Top-Down is Visual Perception? featuring new data (VSS Poster): Attentional Cycles in Detecting Simple Events within Complex Displays Sunday PM Poster #36.301, VSS 2014 Thomas Sanocki,

More information

Analysis of Variance ANOVA

Analysis of Variance ANOVA Analysis of Variance ANOVA Overview We ve used the t -test to compare the means from two independent groups. Now we ve come to the final topic of the course: how to compare means from more than two populations.

More information

Practice Test SHM with Answers

Practice Test SHM with Answers Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one

More information

ANALYSIS OF TREND CHAPTER 5

ANALYSIS OF TREND CHAPTER 5 ANALYSIS OF TREND CHAPTER 5 ERSH 8310 Lecture 7 September 13, 2007 Today s Class Analysis of trends Using contrasts to do something a bit more practical. Linear trends. Quadratic trends. Trends in SPSS.

More information

Determining the Acceleration Due to Gravity

Determining the Acceleration Due to Gravity Chabot College Physics Lab Scott Hildreth Determining the Acceleration Due to Gravity Introduction In this experiment, you ll determine the acceleration due to earth s gravitational force with three different

More information

Cumulative Diagrams: An Example

Cumulative Diagrams: An Example Cumulative Diagrams: An Example Consider Figure 1 in which the functions (t) and (t) denote, respectively, the demand rate and the service rate (or capacity ) over time at the runway system of an airport

More information

INTERFERENCE OF SOUND WAVES

INTERFERENCE OF SOUND WAVES 2011 Interference - 1 INTERFERENCE OF SOUND WAVES The objectives of this experiment are: To measure the wavelength, frequency, and propagation speed of ultrasonic sound waves. To observe interference phenomena

More information

CHAPTER 5 PREDICTIVE MODELING STUDIES TO DETERMINE THE CONVEYING VELOCITY OF PARTS ON VIBRATORY FEEDER

CHAPTER 5 PREDICTIVE MODELING STUDIES TO DETERMINE THE CONVEYING VELOCITY OF PARTS ON VIBRATORY FEEDER 93 CHAPTER 5 PREDICTIVE MODELING STUDIES TO DETERMINE THE CONVEYING VELOCITY OF PARTS ON VIBRATORY FEEDER 5.1 INTRODUCTION The development of an active trap based feeder for handling brakeliners was discussed

More information

International Year of Light 2015 Tech-Talks BREGENZ: Mehmet Arik Well-Being in Office Applications Light Measurement & Quality Parameters

International Year of Light 2015 Tech-Talks BREGENZ: Mehmet Arik Well-Being in Office Applications Light Measurement & Quality Parameters www.led-professional.com ISSN 1993-890X Trends & Technologies for Future Lighting Solutions ReviewJan/Feb 2015 Issue LpR 47 International Year of Light 2015 Tech-Talks BREGENZ: Mehmet Arik Well-Being in

More information

One- and Two-dimensional Motion

One- and Two-dimensional Motion PHYS-101 LAB-02 One- and Two-dimensional Motion 1. Objective The objectives of this experiment are: to measure the acceleration of gravity using one-dimensional motion to demonstrate the independence of

More information

SAM PuttLab. Reports Manual. Version 5

SAM PuttLab. Reports Manual. Version 5 SAM PuttLab Reports Manual Version 5 Reference The information contained in this document is subject to change without notice. The software described in this document is furnished under a license agreement.

More information

Rotational Motion: Moment of Inertia

Rotational Motion: Moment of Inertia Experiment 8 Rotational Motion: Moment of Inertia 8.1 Objectives Familiarize yourself with the concept of moment of inertia, I, which plays the same role in the description of the rotation of a rigid body

More information

Fractional Distillation and Gas Chromatography

Fractional Distillation and Gas Chromatography Fractional Distillation and Gas Chromatography Background Distillation The previous lab used distillation to separate a mixture of hexane and toluene based on a difference in boiling points. Hexane boils

More information

Interference. Physics 102 Workshop #3. General Instructions

Interference. Physics 102 Workshop #3. General Instructions Interference Physics 102 Workshop #3 Name: Lab Partner(s): Instructor: Time of Workshop: General Instructions Workshop exercises are to be carried out in groups of three. One report per group is due by

More information

Pre-lab Quiz/PHYS 224 Magnetic Force and Current Balance. Your name Lab section

Pre-lab Quiz/PHYS 224 Magnetic Force and Current Balance. Your name Lab section Pre-lab Quiz/PHYS 224 Magnetic Force and Current Balance Your name Lab section 1. What do you investigate in this lab? 2. Two straight wires are in parallel and carry electric currents in opposite directions

More information

Force on Moving Charges in a Magnetic Field

Force on Moving Charges in a Magnetic Field [ Assignment View ] [ Eðlisfræði 2, vor 2007 27. Magnetic Field and Magnetic Forces Assignment is due at 2:00am on Wednesday, February 28, 2007 Credit for problems submitted late will decrease to 0% after

More information

Acceleration of Gravity Lab Basic Version

Acceleration of Gravity Lab Basic Version Acceleration of Gravity Lab Basic Version In this lab you will explore the motion of falling objects. As an object begins to fall, it moves faster and faster (its velocity increases) due to the acceleration

More information

Convention Paper Presented at the 118th Convention 2005 May 28 31 Barcelona, Spain

Convention Paper Presented at the 118th Convention 2005 May 28 31 Barcelona, Spain Audio Engineering Society Convention Paper Presented at the 118th Convention 25 May 28 31 Barcelona, Spain 6431 This convention paper has been reproduced from the author s advance manuscript, without editing,

More information

Under 20 of rotation the accuracy of data collected by 2D software is maintained?

Under 20 of rotation the accuracy of data collected by 2D software is maintained? Under 20 of rotation the accuracy of data collected by 2D software is maintained? Introduction This study was undertaken in order to validate the Quintic two-dimensional software. Unlike threedimensional

More information

Alerts & Filters in Power E*TRADE Pro Strategy Scanner

Alerts & Filters in Power E*TRADE Pro Strategy Scanner Alerts & Filters in Power E*TRADE Pro Strategy Scanner Power E*TRADE Pro Strategy Scanner provides real-time technical screening and backtesting based on predefined and custom strategies. With custom strategies,

More information

Section A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1. Page 1 of 11. EduPristine CMA - Part I

Section A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1. Page 1 of 11. EduPristine CMA - Part I Index Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1 EduPristine CMA - Part I Page 1 of 11 Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting

More information

X X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)

X X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1) CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.

More information

10 tips for servos and steppers a simple guide

10 tips for servos and steppers a simple guide 10 tips for servos and steppers a simple guide What are the basic application differences between servos and steppers? Where would you choose one over the other? This short 10 point guide, offers a simple

More information

Lecture 14. Point Spread Function (PSF)

Lecture 14. Point Spread Function (PSF) Lecture 14 Point Spread Function (PSF), Modulation Transfer Function (MTF), Signal-to-noise Ratio (SNR), Contrast-to-noise Ratio (CNR), and Receiver Operating Curves (ROC) Point Spread Function (PSF) Recollect

More information

Prelab Exercises: Hooke's Law and the Behavior of Springs

Prelab Exercises: Hooke's Law and the Behavior of Springs 59 Prelab Exercises: Hooke's Law and the Behavior of Springs Study the description of the experiment that follows and answer the following questions.. (3 marks) Explain why a mass suspended vertically

More information

Section 1.1 Linear Equations: Slope and Equations of Lines

Section 1.1 Linear Equations: Slope and Equations of Lines Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of

More information

STATIC AND KINETIC FRICTION

STATIC AND KINETIC FRICTION STATIC AND KINETIC FRICTION LAB MECH 3.COMP From Physics with Computers, Vernier Software & Technology, 2000. INTRODUCTION If you try to slide a heavy box resting on the floor, you may find it difficult

More information

CELL PHONE INDUCED PERCEPTUAL IMPAIRMENTS DURING SIMULATED DRIVING

CELL PHONE INDUCED PERCEPTUAL IMPAIRMENTS DURING SIMULATED DRIVING CELL PHONE INDUCED PERCEPTUAL IMPAIRMENTS DURING SIMULATED DRIVING David L. Strayer, Frank A. Drews, Robert W. Albert, and William A. Johnston Department of Psychology University of Utah Salt Lake City,

More information

Exploring Magnetism. DataQuest

Exploring Magnetism. DataQuest Exploring Magnetism Magnetism is the force of attraction or repulsion between a magnet and something else. Magnets attract materials made of iron, nickel, or cobalt. Can you think of five things to which

More information

Waves: Recording Sound Waves and Sound Wave Interference (Teacher s Guide)

Waves: Recording Sound Waves and Sound Wave Interference (Teacher s Guide) Waves: Recording Sound Waves and Sound Wave Interference (Teacher s Guide) OVERVIEW Students will measure a sound wave by placing the Ward s DataHub microphone near one tuning fork A440 (f=440hz). Then

More information

Lab #4 - Linear Impulse and Momentum

Lab #4 - Linear Impulse and Momentum Purpose: Lab #4 - Linear Impulse and Momentum The objective of this lab is to understand the linear and angular impulse/momentum relationship. Upon completion of this lab you will: Understand and know

More information