# Determining the Angular Velocity of Winks using High Speed Video. Yan Wang. 5/14/ Measurement and Instrumentation Prof.

Save this PDF as:

Size: px
Start display at page:

Download "Determining the Angular Velocity of Winks using High Speed Video. Yan Wang. 5/14/ Measurement and Instrumentation Prof."

## Transcription

1 Thursday 2-5 Determining the Angular Velocity of Winks using High Speed Video Yan Wang 5/14/ Measurement and Instrumentation Prof. Leonard

2

3 Abstract Tiddlywinks is a strategy game founded in 1955 in Cambridge University. Players, in singles or doubles, attempt to shoot plastic disks called winks into a plastic cup called the pot. Potting winks can sometimes be difficult if the wink is nurdled, which is when the wink is very close to the pot, typically beneath its upper rim. The lexicon of tiddlywinks terminology is exhaustingly extensive and can be found at along with more game information. In this experiment, we measured the angular velocity of a big wink being potted from a nurdled position and compared it to a far position approximately 4 away using high speed video. It was also determined if there was any deceleration during its flight. The results showed a statistically significant difference in angular velocity for the two cases. The angular velocity of the nurdled wink was ± 2.56 rad/s and the angular velocity of the far wink was ± 2.46 rad/s. Although both cases demonstrated a negative mean value for acceleration, they were not statistically significant from zero, indicating only minimal deceleration. These results are consistent with previous findings from experiments done with strobe photography. 1. Introduction In this paper, we measure the angular velocity of a big wink when potted from a nurdled and far position. Potting is one of the most important aspects of tiddlywinks because winks in the pot are worth the most points at the end of the game. Thus, studying how winks behave when they are potted from different locations can provide insight into successfully performing these shots. The analysis of angular velocity is accomplished by analyzing high speed video of each shot using commercial software called LoggerPro. Furthermore, we determine the effect of frictions such as air currents on the wink by examining if there is a decrease in angular velocity during the course of the wink s flight. In the nurdled situation, the wink is partially under the upper rim of the pot. Potting from this position typically requires a rapid wrist flick in order to spin the wink in such a way that it rotates over and above the rim of the pot. In the far situation, the wink is placed approximately 4 away from the pot, which is a common distance for potting. By realizing the actual behavior of the big wink in flight, tiddlywinks players can understand whether at a given distance they should focus on the rotational speed of the wink or some other factors such as the torque being applied and its angle. This experiment extends the work done by Rick Tucker (MIT 80) in 1979 entitled Tiddlywinks Photography 1 in which he uses strobe photography to capture different shots at a maximum of 120fps. He provides qualitative assessments of the behavior of the shots and an approximation of the angular velocity of several potting shots. However, the only potting shot attempts are done with nurdled winks whereas this experiment also observes potting from afar. With advances in video technology, experiments can be performed using high speed video, which is significantly easier because it does not require the specific timing of photography to capture just the right moment. 1

4 2. Background Tiddlywinks combines strategy elements of discrete games such as chess with manual skill that is required for making complex shots. There are four sets of colored winks and games can be played in pairs or singles, where opponents fight to pot their winks while covering their opponent s, which is called squopping. Potting winks scores points (but reduces the number of your winks in play) while squopping obstructs your opponent s ability to play his winks. When potting, a player attempts to flick a wink into the pot with a squidger, which is a larger plastic disk that strikes the wink. These elements of the game are shown in Figure 1 below. Figure 1: Strobe photograph of potting a big wink. The cup is called the pot and the large disk used to strike the wink is called a squidger (source: Robert Ochshorn). Winks come in big and small varieties. They are 22mm and 16mm in diameter, respectively, and approximately 1.5mm thick according to The Official Rules of Tiddlywinks 2. Each player starts with two big winks and four small winks. The pot is 38mm high with an external diameter of 48mm at the top and 38mm at the base. Squidgers are made out of plastic and must be between 25mm and 51mm in diameter and no thicker than 5mm at the edge. The game is played on a 3 feet by 6 feet mat. 2.1 Angular Velocity and Acceleration To calculate the angular velocity of a wink about its center using vectors that describe the positions of its front (f) and back (b) lips, we define angles θ 0 and θ 1 as shown in Figure 2, which shows side views of a wink in two discrete time states. The position, (x, y), of the front and back lips are also shown. They are measured with respect to a common origin. 2

5 (x 0 f, y 0 f ) (x 1 f, y 1 f ) θ 0 θ 1 (x 0 b, y 0 b ) (x 1 b, y 1 b ) t 0 t 1 Figure 2: Angle and position of wink in two states with respect to the vertical. Equation 1 defines θ 0 and θ 1 by the position of the front and back lips of the wink, where a positive angle is measured counter-clockwise from the vertical. tan, 0,1. (1) By definition, angular velocity is the change in angle per unit change in time. We report a clockwise change in angle as positive because the wink rotates in a clockwise direction in our videos. We can define ω, angular velocity, as the total change in angle divided by the change in time, which is shown in Equation 2:. (2) Angular acceleration, α, is the derivative of angular velocity. If we have angular velocities measured over time, the slope of the line relating angular velocity to time is the acceleration. Equation 3 defines acceleration as a function of angular velocity.. (3) 2.2 Verifying Camera Output with Gravity The digital video file output of our Phantom 640 camcorder is 10 frames per second (fps) with an actual recording rate of 500fps. Thus, the file s timestamps must be multiplied by 1/50 to convert to the real time that is shown in each frame. This can be verified by performing a check on gravity using one of the videos. Winks in flight can be described by a parabolic trajectory according to basic kinematics. Equation 4 defines the vertical position, y, of an object as a function of time: 1 2, (4) where y 0 is the initial height, v 0 is the initial velocity in the y direction, g is the acceleration due to gravity, and t is time. 3

6 If we fit a curve to vertical location of the wink in the digital video file, we should find that the constant in front of the t 2 term should be approximately (1/2)(1/50) 2 of the value of g (approximately m/s 2 ). 3. Experimental Procedure A standard big red wink was selected for the experiment and placed at a nurdled and far (approximately 4 ) position for each video. The squidger used for potting the wink belonged to the author and is 44mm in diameter and of medium edge sharpness. A Phantom 640 digital camcorder was used to record the path of the wink into the pot at the following settings: 500fps, 200μs exposure time, 800x600 resolution, and non-interlaced mode. Two large halogen lamps were also used to provide extra lighting because the exposure time of each frame at high frame rates is very limited. The scale that we used for the analysis was the diameter of the pot, which is 51mm. Figure 3 shows a diagram and photo of our experimental setup. Figure 3: Schematic (not to scale) and photo of the experimental setup. The pot and wink cannot be seen in the photograph due to the overwhelming effect of the halogen lamps. Samples from the videos are shown in Figure 4 for each of the positions that we successfully potted from. The far wink is on the left and the nurdled wink is on the right. Figure 4: Screen capture from the Phantom 640 s video of the experimental setup immediately before potting in their original coloration. 4

7 A video clip was recorded of a successful pot from each position. This video was then imported into LoggerPro for analysis using its movie feature. After defining an origin at the back lip of the wink, data points were selected for the positions of the back and front lips of the wink during its flight, which created the position vectors necessary for our measurements. Calculation of angular velocity and its error was performed in Microsoft Excel. MathCAD was used to determine the best fit line, its slope, and its error in order to determine if there were significant frictional forces acting on the wink. Finally, a parabola was fit to the far wink s path with LoggerPro to check the value of g and verify that our time conversion was correct (see Section 2.2). This was done by taking the constant value in front of the t 2 term and multiplying by 2*50 2 while accounting for the error. The value of gravity derived from this was ± 0.04 m/s 2, which is reasonably close to the accepted value of m/s Results and Discussion The angular velocity of the far wink was greater than that of the nurdled wink. Velocity was measured to be ± 2.46 rad/s and ± 2.56 rad/s, respectively. These values are the averages of the velocities over the course of the wink s flight. Angular acceleration, as determined by the slope of the best fit line, was ± rad/s 2 for the far wink and ± rad/s 2 for the nurdled wink. Although both values are negative and indicate deceleration, which is what we would expect, the confidence intervals are too large to make it statistically significant from zero or each other. These results are summarized in Table 1. Units Nurdled Wink Far Wink ω rad/s ± ± 2.46 α rad/s ± ± Table 1: Summary of the angular velocities and accelerations of the nurdled and far winks. It is important to note that some data points were not used in the analysis. Any negative angular velocities were removed because it does not make sense for the rotation to instantly reverse direction. Extremely high and low angular velocities were also removed because it caused the data to be discontinuous. These factors resulted in the removal of nine points from the nurdled wink data set and six points from the far wink data set. Figures 5 and 6 show the resulting data and the best fit lines. 5

8 140 Angular Velocity (rad/s) n= 128, Δt = 0.262s Time (s) Figure 5: Angular velocity of nurdled big wink. 140 Angular Velocity (rad/s) n= 80, Δt = 0.162s Time (s) Figure 6: Angular velocity of far big wink. Figures 5 and 6 show that the data had a great amount of variance in both cases, which results in very large error ranges for the slopes (acceleration). This difficulty arose from manually judging the position of the front and back lips in LoggerPro when constructing our data set. In the future, more lighting, a white background, and a white-sleeved shirt could improve the clarity of the wink in the video and yield better results for angular acceleration measurements. The error of the angular velocities was relatively low because of the law of large numbers. Because the sample size was large in both cases, the error decreased tremendously. Using a higher frame rate would result in more data points and further reduce the error. 6

9 The nurdled wink results are consistent with the findings in Tiddlywinks Photography. In his Photo 1 and Slide 3/20, Tucker found that a nurdled wink performed a half rotation in 1/24s and 1/30s, respectively. This is equal to 75 rad/s and 94 rad/s, respectively, and our result of ± 2.56 rad/s lies within this range. One limitation of Tucker s work is that it does not measure the angular velocity of winks that are not nurdled, which would provide useful data for comparison with our results and nurdled winks. One possible explanation for why the angular velocity of a nurdled wink is less than that of a far wink is the amount of torque that must be applied to pot the wink. A farther wink would require more torque and thus result in a greater angular velocity. However, slight variations in the angle of the moment arm, which is determined by the squidger angle at the time of release, could also affect the results. It is difficult to determine if the small difference we found in angular velocities was due to torque differences or human inconsistency without a mechanical potting device. Such a machine could be constructed in the future to aid analysis. 5. Conclusions and Recommendations The purpose of this experiment was to measure and compare the angular velocities of a nurdled wink and far wink. We found that the angular velocity of a far wink was greater than that of a nurdled wink when potting. The angular velocities were ± 2.46 rad/s and ± 2.56 rad/s, respectively. Although both cases demonstrated a negative mean value for acceleration, they were not statistically significant from zero, indicating only minimal deceleration. Our findings are consistent with Tucker s measurements of the angular velocity of nurdled winks. Utilizing frame rates greater than 500fps and more lighting could also decrease the error in the angular acceleration measurements. An even simpler adjustment would be to use a white background and wear a white-sleeved shirt. Finally, the construction of a mechanical potting device would be extremely useful for the purpose of repeatability. Acknowledgements The author would like to thank Dr. Jim Bales and the Edgerton Center at MIT for the use of their high speed camcorder. A great deal of assistance and advice was provided by Professor John Leonard and Dr. Barbara Hughey of during the course of this project. Finally, Robert Ochshorn has allowed me to use his amazing strobe photograph (Figure 1) in numerous applications over the years to promote tiddlywinks. References 1 R. Tucker, Tiddlywinks Photography, Strobe Project Laboratory Project Report, MIT, Fall, 1979 (unpublished). 2 The Official Rules of Tiddlywinks, English Tiddlywinks Association, April, 2005 (www.etwa.org). 7

### Measuring the Earth s Diameter from a Sunset Photo

Measuring the Earth s Diameter from a Sunset Photo Robert J. Vanderbei Operations Research and Financial Engineering, Princeton University rvdb@princeton.edu ABSTRACT The Earth is not flat. We all know

### 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

### Section 10.7 Parametric Equations

299 Section 10.7 Parametric Equations Objective 1: Defining and Graphing Parametric Equations. Recall when we defined the x- (rcos(θ), rsin(θ)) and y-coordinates on a circle of radius r as a function of

### 2.7 A GOOD RETURN 2.7.1 The ball, having been served or returned, shall be struck so that it passes over or around the net

Table Tennis 2. Laws - The Rules of the Game 2.1 THE TABLE 2.1.1 The upper surface of the table, known as the playing surface, shall be rectangular, 2.74m long and 1.525m wide, and shall lie in a horizontal

### TABLE TENNIS SINGLES RULES

TABLE TENNIS SINGLES RULES Table Tennis Singles Rules 1) Elimination Tournament. 2) One player per team. 3) Play best of 3 games. Games to 21, unless ties at 20. In that case, alternate service and must

### PHY121 #8 Midterm I 3.06.2013

PHY11 #8 Midterm I 3.06.013 AP Physics- Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension

### Visual Physics 218 Projectile Motion [Lab 2]

In this experiment, you will be using your video equipment to evaluate two-dimensional motion. It will be necessary to plot the data in an xy-coordinate system and separate the data into x and y components.

### No Brain Too Small PHYSICS. 2 kg

MECHANICS: ANGULAR MECHANICS QUESTIONS ROTATIONAL MOTION (2014;1) Universal gravitational constant = 6.67 10 11 N m 2 kg 2 (a) The radius of the Sun is 6.96 10 8 m. The equator of the Sun rotates at a

### Solution Derivations for Capa #11

Solution Derivations for Capa #11 1) A horizontal circular platform (M = 128.1 kg, r = 3.11 m) rotates about a frictionless vertical axle. A student (m = 68.3 kg) walks slowly from the rim of the platform

### Wind Turbines. Wind Turbines 2. Wind Turbines 4. Wind Turbines 3. Wind Turbines 5. Wind Turbines 6

Wind Turbines 1 Wind Turbines 2 Introductory Question Wind Turbines You and a child half your height lean out over the edge of a pool at the same angle. If you both let go simultaneously, who will tip

### 5.1 Vector and Scalar Quantities. A vector quantity includes both magnitude and direction, but a scalar quantity includes only magnitude.

Projectile motion can be described by the horizontal ontal and vertical components of motion. In the previous chapter we studied simple straight-line motion linear motion. Now we extend these ideas to

### The playing surface shall not include the vertical sides of the tabletop.

Table Tennis Rules Table Definition The upper surface of the table, known as the playing surface, shall be rectangular, 2.74m long and 1.525m wide, and shall lie in a horizontal plane 76cm above the floor.

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 3 - ROTATING SYSTEMS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 3 - ROTATING SYSTEMS TUTORIAL 1 - ANGULAR MOTION CONTENT Be able to determine the characteristics

### 5.2 Rotational Kinematics, Moment of Inertia

5 ANGULAR MOTION 5.2 Rotational Kinematics, Moment of Inertia Name: 5.2 Rotational Kinematics, Moment of Inertia 5.2.1 Rotational Kinematics In (translational) kinematics, we started out with the position

### General rules for Table Tennis

General rules for Table Tennis 2.01 The Table 2.01.01 The upper surface of the table, known as the playing surface, shall be rectangular, 2.74m long and 1.525m wide, and shall lie in a horizontal plane

### Physics 201. Fall 2009. Two Dimensional Motion Due Friday November 6, 2009

Physics 201 Fall 2009 Two Dimensional Motion Due Friday November 6, 2009 Points: 30 Name Partners This is a more detailed lab experiment than the exercises you have done in the class in the past. You will

### Lab 8: Ballistic Pendulum

Lab 8: Ballistic Pendulum Equipment: Ballistic pendulum apparatus, 2 meter ruler, 30 cm ruler, blank paper, carbon paper, masking tape, scale. Caution In this experiment a steel ball is projected horizontally

### 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

### POLAR COORDINATES DEFINITION OF POLAR COORDINATES

POLAR COORDINATES DEFINITION OF POLAR COORDINATES Before we can start working with polar coordinates, we must define what we will be talking about. So let us first set us a diagram that will help us understand

### 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

### 2 THE LAWS OF TABLE TENNIS

2 THE LAWS OF TABLE TENNIS 2.1 THE TABLE 2.1.1 The upper surface of the table, known as the playing surface, shall be rectangular, 2.74m long and 1.525m wide, and shall lie in a horizontal plane 76cm above

### TABLE TENNIS TABLE TENNIS

1 The Official Special Olympics Sports Rules for Table Tennis shall govern all Special Olympics competitions. As an international sports program, Special Olympics has created these rules based upon International

### Chapter 4. Kinematics - Velocity and Acceleration. 4.1 Purpose. 4.2 Introduction

Chapter 4 Kinematics - Velocity and Acceleration 4.1 Purpose In this lab, the relationship between position, velocity and acceleration will be explored. In this experiment, friction will be neglected.

### Experiment 8 ~ Rotational and Translational Energies

Experiment 8 ~ Rotational and Translational Energies Purpose: The objective of this experiment is to examine the conversion of gravitational potential energy to different types of energy: translational,

### 5.1-Angles and Their Measure

5.1-Angles and Their Measure Objectives: 1. Find the degree or radian measure of co-terminal angles. 2. Convert between degrees minutes and seconds and decimal degrees. 3. Convert between degrees and radians.

### Physics 2048 Test 1 Solution (solutions to problems 2-5 are from student papers) Problem 1 (Short Answer: 20 points)

Physics 248 Test 1 Solution (solutions to problems 25 are from student papers) Problem 1 (Short Answer: 2 points) An object's motion is restricted to one dimension along the distance axis. Answer each

### 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,

### 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

### 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

### Jump Shot Mathematics Howard Penn

Jump Shot Mathematics Howard Penn Abstract In this paper we exae variations of standard calculus problems in the context of shooting a basketball jump shot. We believe that many students will find this

### 2 THE LAWS OF TABLE TENNIS

2 THE LAWS OF TABLE TENNIS 2.1 THE TABLE 2.1.1 The upper surface of the table, known as the playing surface, shall be rectangular, 2.74m long and 1.525m wide, and shall lie in a horizontal plane 76cm above

### Rotational Inertia Demonstrator

WWW.ARBORSCI.COM Rotational Inertia Demonstrator P3-3545 BACKGROUND: The Rotational Inertia Demonstrator provides an engaging way to investigate many of the principles of angular motion and is intended

### 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

### High-speed Photography with a Still Digital Camera

High-speed Photography with a Still Digital Camera Matthew Moore North Carolina School of Science and Math 1219 Broad St. Durham, NC 27705 Sponsored By Dr. Loren Winters 12/2/99 Abstract High-speed photography

### The lab entitled Launching Lab has been designed to help aid in the visualization and application of various linear and projectile motion equations

The lab entitled Launching Lab has been designed to help aid in the visualization and application of various linear and projectile motion equations used in Physics II class at ERHS. The linear motion equations

### 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

### 1 of 7 9/5/2009 6:12 PM

1 of 7 9/5/2009 6:12 PM Chapter 2 Homework Due: 9:00am on Tuesday, September 8, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]

### Rotation: Moment of Inertia and Torque

Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn

### Chapter 24 Physical Pendulum

Chapter 4 Physical Pendulum 4.1 Introduction... 1 4.1.1 Simple Pendulum: Torque Approach... 1 4. Physical Pendulum... 4.3 Worked Examples... 4 Example 4.1 Oscillating Rod... 4 Example 4.3 Torsional Oscillator...

### OUTCOME 2 KINEMATICS AND DYNAMICS TUTORIAL 2 PLANE MECHANISMS. You should judge your progress by completing the self assessment exercises.

Unit 60: Dynamics of Machines Unit code: H/601/1411 QCF Level:4 Credit value:15 OUTCOME 2 KINEMATICS AND DYNAMICS TUTORIAL 2 PLANE MECHANISMS 2 Be able to determine the kinetic and dynamic parameters of

### Lab 5: Conservation of Energy

Lab 5: Conservation of Energy Equipment SWS, 1-meter stick, 2-meter stick, heavy duty bench clamp, 90-cm rod, 40-cm rod, 2 double clamps, brass spring, 100-g mass, 500-g mass with 5-cm cardboard square

### What you need to know to play a fun game of ping-pong

What you need to know to play a fun game of ping-pong Sometimes all you want to know are the basic rules to play a friendly match of ping pong. This section is for you. If you want more offical rules,

### Power Electronics. Prof. K. Gopakumar. Centre for Electronics Design and Technology. Indian Institute of Science, Bangalore.

Power Electronics Prof. K. Gopakumar Centre for Electronics Design and Technology Indian Institute of Science, Bangalore Lecture - 1 Electric Drive Today, we will start with the topic on industrial drive

### Shear Force and Moment Diagrams

C h a p t e r 9 Shear Force and Moment Diagrams In this chapter, you will learn the following to World Class standards: Making a Shear Force Diagram Simple Shear Force Diagram Practice Problems More Complex

### Speed, velocity and acceleration

Chapter Speed, velocity and acceleration Figure.1 What determines the maximum height that a pole-vaulter can reach? 1 In this chapter we look at moving bodies, how their speeds can be measured and how

### Chapter 10: Linear Kinematics of Human Movement

Chapter 10: Linear Kinematics of Human Movement Basic Biomechanics, 4 th edition Susan J. Hall Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University Objectives Discuss the interrelationship

### Awell-known lecture demonstration1

Acceleration of a Pulled Spool Carl E. Mungan, Physics Department, U.S. Naval Academy, Annapolis, MD 40-506; mungan@usna.edu Awell-known lecture demonstration consists of pulling a spool by the free end

### Angular acceleration α

Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 7-0 Linear and Circular Motion Compared Slide 7- Linear and Circular Kinematics Compared Slide 7-

### Chapter 6 Work and Energy

Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system

### Trigonometry Chapter 3 Lecture Notes

Ch Notes Morrison Trigonometry Chapter Lecture Notes Section. Radian Measure I. Radian Measure A. Terminology When a central angle (θ) intercepts the circumference of a circle, the length of the piece

### 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

### Acceleration due to Gravity

Acceleration due to Gravity 1 Object To determine the acceleration due to gravity by different methods. 2 Apparatus Balance, ball bearing, clamps, electric timers, meter stick, paper strips, precision

### SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS

SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering

### v v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )

Week 3 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

### LESSON TITLE: Math in Basketball (by Deborah L. Ives, Ed.D) GRADE LEVEL/COURSE: Grades 7-12 Algebra. TIME ALLOTMENT: Two 45-minute class periods

LESSON TITLE: Math in Basketball (by Deborah L. Ives, Ed.D) GRADE LEVEL/COURSE: Grades 7-12 Algebra TIME ALLOTMENT: Two 45-minute class periods OVERVIEW Using video segments and web interactives from Get

### 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

### Chapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.

Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems

### Physics 201 Homework 8

Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 N-m is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kg-m 2. What is the

### Chapter 13, example problems: x (cm) 10.0

Chapter 13, example problems: (13.04) Reading Fig. 13-30 (reproduced on the right): (a) Frequency f = 1/ T = 1/ (16s) = 0.0625 Hz. (since the figure shows that T/2 is 8 s.) (b) The amplitude is 10 cm.

### KIN Biomechanics

KIN 335 - Biomechanics LAB: Center of Mass (Center of Gravity) of the Human Body Reading Assignment: Bishop, R.D. & Hay, J.G. (1979). Basketball: the mechanics of hanging in the air. Medicine and Science

### Motorcycle Sliding Coefficient of Friction Tests

Motorcycle Sliding Coefficient of Friction Tests Bruce F. McNally, ACTAR Northeast Collision Analysis, Inc. Wade Bartlett, PE, ACTAR Mechanical Forensic Engineering Services, LLP Presented at the 21 st

### Lab 7: Rotational Motion

Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125

### Lab # 3 - Angular Kinematics

Purpose: Lab # 3 - Angular Kinematics The objective of this lab is to understand the relationship between segment angles and joint angles. Upon completion of this lab you will: Understand and know how

### Chapter 18 Static Equilibrium

Chapter 8 Static Equilibrium 8. Introduction Static Equilibrium... 8. Lever Law... Example 8. Lever Law... 4 8.3 Generalized Lever Law... 5 8.4 Worked Examples... 7 Example 8. Suspended Rod... 7 Example

### Physics of the tractor pull. How to use the tractor pull as a context rich setting to cover Minnesota Physical Science Standards.

Physics of the tractor pull. How to use the tractor pull as a context rich setting to cover Minnesota Physical Science Standards. Richard Lahti, Assistant Professor of Chemistry and Physics at Minnesota

### Tennessee State University

Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.

### Solution: Angular velocity in consistent units (Table 8.1): 753.8. Velocity of a point on the disk: Rate at which bits pass by the read/write head:

Problem P8: The disk in a computer hard drive spins at 7200 rpm At the radius of 0 mm, a stream of data is magnetically written on the disk, and the spacing between data bits is 25 μm Determine the number

### Catapult Engineering Pilot Workshop. LA Tech STEP 2007-2008

Catapult Engineering Pilot Workshop LA Tech STEP 2007-2008 Some Background Info Galileo Galilei (1564-1642) did experiments regarding Acceleration. He realized that the change in velocity of balls rolling

### Chapter 3.8 & 6 Solutions

Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled

### CHAPTER 28 THE CIRCLE AND ITS PROPERTIES

CHAPTER 8 THE CIRCLE AND ITS PROPERTIES EXERCISE 118 Page 77 1. Calculate the length of the circumference of a circle of radius 7. cm. Circumference, c = r = (7.) = 45.4 cm. If the diameter of a circle

### Physics 126 Practice Exam #3 Professor Siegel

Physics 126 Practice Exam #3 Professor Siegel Name: Lab Day: 1. Which one of the following statements concerning the magnetic force on a charged particle in a magnetic field is true? A) The magnetic force

### Physics Section 3.2 Free Fall

Physics Section 3.2 Free Fall Aristotle Aristotle taught that the substances making up the Earth were different from the substance making up the heavens. He also taught that dynamics (the branch of physics

### C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

### Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide)

Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide) 2012 WARD S Science v.11/12 OVERVIEW Students will measure

### 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

### The Physics and Math of Ping-pong and How It Affects Game Play. By: Connor Thompson & Andrew Johnson

The Physics and Math of Ping-pong and How It Affects Game Play 1 The Physics and Math of Ping-pong and How It Affects Game Play By: Connor Thompson & Andrew Johnson The Practical Applications of Advanced

### WEIGHTLESS WONDER Reduced Gravity Flight

WEIGHTLESS WONDER Reduced Gravity Flight Instructional Objectives Students will use trigonometric ratios to find vertical and horizontal components of a velocity vector; derive a formula describing height

### ELEMENTS OF VECTOR ALGEBRA

ELEMENTS OF VECTOR ALGEBRA A.1. VECTORS AND SCALAR QUANTITIES We have now proposed sets of basic dimensions and secondary dimensions to describe certain aspects of nature, but more than just dimensions

### 2After completing this chapter you should be able to

After completing this chapter you should be able to solve problems involving motion in a straight line with constant acceleration model an object moving vertically under gravity understand distance time

### Response to Harmonic Excitation Part 2: Damped Systems

Response to Harmonic Excitation Part 2: Damped Systems Part 1 covered the response of a single degree of freedom system to harmonic excitation without considering the effects of damping. However, almost

### 3 Work, Power and Energy

3 Work, Power and Energy At the end of this section you should be able to: a. describe potential energy as energy due to position and derive potential energy as mgh b. describe kinetic energy as energy

### Practice Exam Three Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Practice Exam Three Solutions Problem 1a) (5 points) Collisions and Center of Mass Reference Frame In the lab frame,

### Orbital Mechanics. Angular Momentum

Orbital Mechanics The objects that orbit earth have only a few forces acting on them, the largest being the gravitational pull from the earth. The trajectories that satellites or rockets follow are largely

### 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

Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

### Chapter 8: Rotational Motion of Solid Objects

Chapter 8: Rotational Motion of Solid Objects 1. An isolated object is initially spinning at a constant speed. Then, although no external forces act upon it, its rotational speed increases. This must be

### Physics 1020 Laboratory #6 Equilibrium of a Rigid Body. Equilibrium of a Rigid Body

Equilibrium of a Rigid Body Contents I. Introduction II. III. IV. Finding the center of gravity of the meter stick Calibrating the force probe Investigation of the angled meter stick V. Investigation of

### Physics 1A Lecture 10C

Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. --Oprah Winfrey Static Equilibrium

### Uniformly Accelerated Motion

Uniformly Accelerated Motion Under special circumstances, we can use a series of three equations to describe or predict movement V f = V i + at d = V i t + 1/2at 2 V f2 = V i2 + 2ad Most often, these equations

### Lecture Presentation Chapter 7 Rotational Motion

Lecture Presentation Chapter 7 Rotational Motion Suggested Videos for Chapter 7 Prelecture Videos Describing Rotational Motion Moment of Inertia and Center of Gravity Newton s Second Law for Rotation Class

### Physics Midterm Review Packet January 2010

Physics Midterm Review Packet January 2010 This Packet is a Study Guide, not a replacement for studying from your notes, tests, quizzes, and textbook. Midterm Date: Thursday, January 28 th 8:15-10:15 Room:

### Stability Of Structures: Basic Concepts

23 Stability Of Structures: Basic Concepts ASEN 3112 Lecture 23 Slide 1 Objective This Lecture (1) presents basic concepts & terminology on structural stability (2) describes conceptual procedures for

### Lab M1: The Simple Pendulum

Lab M1: The Simple Pendulum Introduction. The simple pendulum is a favorite introductory exercise because Galileo's experiments on pendulums in the early 1600s are usually regarded as the beginning of

### Image Formation Principle

Image Formation Principle Michael Biddle Robert Dawson Department of Physics and Astronomy The University of Georgia, Athens, Georgia 30602 (Dated: December 8, 2015) The aim of this project was to demonstrate

### 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

### 1 of 10 11/23/2009 6:37 PM

hapter 14 Homework Due: 9:00am on Thursday November 19 2009 Note: To understand how points are awarded read your instructor's Grading Policy. [Return to Standard Assignment View] Good Vibes: Introduction

### QUANTITATIVE MEASUREMENT OF TEAMWORK IN BALL GAMES USING DOMINANT REGION

QUANTITATIVE MEASUREMENT OF TEAMWORK IN BALL GAMES USING DOMINANT REGION Tsuyoshi TAKI and Jun-ichi HASEGAWA Chukyo University, Japan School of Computer and Cognitive Sciences {taki,hasegawa}@sccs.chukyo-u.ac.jp

### Lecture L5 - Other Coordinate Systems

S. Widnall, J. Peraire 16.07 Dynamics Fall 008 Version.0 Lecture L5 - Other Coordinate Systems In this lecture, we will look at some other common systems of coordinates. We will present polar coordinates