ANGULAR POSITION. 4. Rotational Kinematics and Dynamics


 Janis Lane
 2 years ago
 Views:
Transcription
1 ANGULAR POSITION To describe rotational motion, we define angular quantities that are analogous to linear quantities Consider a bicycle wheel that is free to rotate about its axle The axle is the axis of rotation for the wheel If there is a small spot of red paint on the tire, we can use this reference to describe its rotational motion The angular position of the spot is the angle θ, that a line from the axle to the spot makes with a reference line SI unit is the radian (rad) θ > 0 anticlockwise rotation: θ < 0 clockwise rotation A radian is the angle for which the arc length, s, on a circle of radius r is equal to the radius of the circle The arc length s for an arbitrary angle θ measured in radians is s = r θ 1 revolution is 360 = 2π rad 1 rad = 360 /2π =
2 ANGULAR VELOCITY As the bicycle wheel rotates, the angular position of the spot changes Angular displacement is θ = θ f θ i Average angular velocity is ω av = θ/ t (rad/s) Analogous average linear velocity v av = x/ t Instantaneous angular velocity is the limit of ω av as the time interval t reaches zero ω > 0 anticlockwise rotation: ω < 0 clockwise rotation The time to complete one revolution is known as the period, T T = 2π/ω seconds 2
3 ANGULAR ACCELERATION If the angular velocity of the rotating bicycle wheel increases or decreases with time, the wheel experiences an angular acceleration, α The average angular acceleration is the change in angular velocity in a given time interval α av = ω/ t rad/s 2 The instantaneous angular acceleration is the limit of α av as the time interval t approaches zero The sign of angular acceleration is determined by whether the change in angular velocity is positive or negative If ω is becoming more positive (ω f > ω i ), α is positive If ω is becoming more negative (ω f < ω i ), α is negative If ω and α have the same sign, speed of rotation increasing If ω and α have opposite signs, speed of rotation decreasing 3
4 ROTATIONAL KINEMATICS Rotational kinematics describes rotational motion Consider the pulley shown below, which has a string wrapped around its circumference with a mass attached to its free end When the mass is released, the pulley begins to rotate slowly at first, then faster and faster The pulley thus accelerates with constant angular acceleration: α = ω/ t If the pulley starts with initial angular velocity ω 0 at time t = 0, and at the later time t the angular velocity is ω then α = ω/ t = (ω ω 0 )/(t t 0 ) = (ω ω 0 )/t Thus the angular velocity ω varies with time as follows: ω = ω 0 + αt Example: If the angular velocity of the pulley is 8.4rad/s at a given time, and its angular acceleration is 2.8rad/s 2, what is the angular velocity of the pulley 1.5s later? 4
5 LINEAR AND ANGULAR ANALOGIES 5
6 ROTATIONAL KINEMATICS: EXAMPLE (1) To throw a curve ball, a baseball pitcher gives the ball an initial speed of 36.0 rad/s. When the catcher gloves the ball 0.595s later, its angular speed has decreased (due to air resistance) to 34.2 rad/s. What is the ball s angular acceleration, assuming it to be constant? How many revolutions does the ball make before being caught? 6
7 ROTATIONAL KINEMATICS: EXAMPLE (2) On a TV game show, contestants spin a wheel when it is their turn. One contestant gives the wheel an initial angular speed of 3.4 rad/s. It then rotates through1 ¼ revolutions and comes to rest on the BANKRUPT space. Find the angular acceleration of the wheel, assuming it to be constant. How long does it take for the wheel to come to a rest? 7
8 TANGENTIAL SPEED OF A ROTATING OBJECT Consider somebody riding a merrygoround, which completes one circuit every T = 7.5s Thus ω = 2π/T = rad/s The path followed is circular, with the centre of the circle at the axis of rotation The rider is moving in a direction that is tangential to the circular path The tangential speed is the speed at a tangent to the circular path, and is found by dividing the circumference by T: v t = 2πr/T m/s Because 2π/T = ω we have: v t = rω m/s Example: Find the angular speed a CD must have to give a linear speed of 1.25m/s when the laser beam shines on the disk 2.50cm and 6.00cm from its centre 8
9 CENTRIPETAL ACCELERATION OF A ROTATING OBJECT When an object moves in a circular path, it experiences a centripetal acceleration, a cp, which is always directed toward the axis of rotation a cp = v 2 /r However v = v t = rω, so a cp = (rω) 2 /r = rω 2 m/s 2 Rotating devices known as centrifuges can produce centripetal accelerations many times greater than gravity, such as those used to train astronauts, or microhematocrit centrifuges used to separate blood cells from plasma Example: In a microhematocrit centrifuge, small samples of blood are placed in capillary tubes. These tubes are rotated at 11,500rpm, with the bottom of the tubes 9.07cm from the axis of rotation. Find the linear speed of the bottom of the tubes. What is the centripetal acceleration at the bottom of the tubes? 9
10 TANGENTIAL AND CENTRIPETAL ACCELERATION When the angular speed of an object in a circular path changes, so does its tangential speed When tangential speed changes, a tangential acceleration is experienced a t If ω changes by the amount ω, with r remaining constant, the corresponding change in tangential speed is v t = r ω If ω occurs in time interval t, then the tangential acceleration is a t = v t / t = r ω/ t Since ω/ t is the angular acceleration α, then the tangential acceleration of a rotating object is given by a t = rα m/s 2 Recall that a t is due to a changing tangential speed, and that a cp is caused by a changing direction of motion (even if a t remains constant) In cases where both tangential and centripetal accelerations are present, the total sum is the vector sum of the two a r a r t and cp are at right angles, hence the magnitude of the total acceleration is a = (a t2 + a cp2 ) The direction is given by φ = tan 1 (a cp /a t ) 10
11 TANGENTIAL AND CENTRIPETAL ACCELERATION: EXAMPLE Suppose the centrifuge above is starting up with a constant angular acceleration of 95.0 rad/s 2. What is the magnitude of the centripetal, tangential and total accelerations of the bottom of a tube when the angular speed is 8.00 rad/s? What angle does the total acceleration make with the direction of motion? 11
12 TORQUE: WHEN FORCE APPLIED IS TANGENTIAL Trying to loosen a nut by rotating a wrench anticlockwise is easier when you apply the force as far away from the nut as possible Likewise to open a revolving door is easier when you push further from the axis of rotation The tendency for a force to cause a rotation increases with the distance r from the axis of rotation to the force Torque is a quantity that takes into account both the magnitude of the force and the distance from the axis of rotation, r Torque: τ = rf Nm (Newton metre) This equation is only valid when the applied force is tangential to a circle of radius r centred on the axis of rotation 12
13 TORQUE: WHEN FORCE APPLIED IS NOT TANGENTIAL Consider pulling on a merrygoround in a direction that is radial (along a line that extends through the axis of rotation) Such a force has no tendency to cause a rotation, and thus the axle simply exerts an equal and opposite force, and thus the merrygoround remains at rest A radial force produces zero torque If the force applied is at an angle θ to the radial line, the vector force F r needs to be resolved into radial and tangential components Radial component magnitude: Fcosθ Tangential component magnitude: Fsinθ Only tangential component causes rotation, thus Fcosθ = 0 General definition of torque: τ = rfsinθ Nm τ > 0 anticlockwise angular acceleration τ < 0 clockwise angular acceleration 13
14 TORQUE: EXAMPLE Two helmsmen, in disagreement about which way to turn a ship, exert different forces on the ship s wheel. The wheel has a radius of 0.74m, and the two forces have the magnitudes F 1 = 72N and F 2 = 58N. Find the torque caused by F r and the torque caused by. In 1 F r 2 which direction does the wheel turn as a result of these two forces. 14
15 TORQUE AND ANGULAR ACCELERATION A single torque, τ, acting on an object causes the object to have an angular acceleration α Consider a small object of mass m connected to an axis of rotation by a light rod of length r If a tangential force of magnitude F is applied to the mass, it will move with an acceleration according to Newton s 2 nd law, a = F/m Linear and angular accelerations related by α = a/r Combining: α = a/r = F/mr Multiplying by r/r gives α = rf/mr 2 Since torque τ = rf, we define a new quantity called the moment of inertia: I = mr 2 Thus α = τ/i or τ = Iα In a system with more than one torque, we take the net sum of all the torques acting: τ net = Στ = Iα Above is Newton s 2 nd law for rotational motion 15
16 MOMENT OF INERTIA I = mr 2 is general case for moment of inertia 16
17 TORQUE AND ANGULAR ACCELERATION: EXAMPLES A light rope wrapped around a disk shaped pulley is pulled tangentially with a force of 0.53N. Find the angular acceleration of the pulley, given that its mass is 1.3kg and its radius is 0.11m. A fisherman is dozing when a fish takes the line and pulls it with a tension T. The spool of the fishing reel is at rest initially and rotates without friction as the fish pulls for time t. If the radius of the spool is R and its moment of inertia is I, find the angular displacement of the spool. Also find the length of line pulled from the spool and the angular speed of the spool. Hint: make use of θ = θ 0 + ω 0 t + ½αt 2 and ω = ω 0 + αt 17
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
More informationLinear 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 informationUnit 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 informationChapter 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
More informationChapter 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
More informationPHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?
1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always
More informationChapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.
Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular
More informationPHY231 Section 1, Form B March 22, 2012
1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate
More informationRotational inertia (moment of inertia)
Rotational inertia (moment of inertia) Define rotational inertia (moment of inertia) to be I = Σ m i r i 2 or r i : the perpendicular distance between m i and the given rotation axis m 1 m 2 x 1 x 2 Moment
More informationLecture 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
More informationEDEXCEL 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
More informationCHAPTER 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
More information11. Rotation Translational Motion: Rotational Motion:
11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational
More informationOUTCOME 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
More informationcircular motion & gravitation physics 111N
circular motion & gravitation physics 111N uniform circular motion an object moving around a circle at a constant rate must have an acceleration always perpendicular to the velocity (else the speed would
More informationSOLID 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
More informationAngular acceleration α
Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 70 Linear and Circular Motion Compared Slide 7 Linear and Circular Kinematics Compared Slide 7
More informationPhysics Honors: Chapter 7 Practice Test
Physics Honors: Chapter 7 Practice Test Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. When an object is moving with uniform circular motion,
More informationIMPORTANT NOTE ABOUT WEBASSIGN:
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
More informationChapter 4 Dynamics: Newton s Laws of Motion
Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the NormalForce
More informationPHY121 #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
More information11. Describing Angular or Circular Motion
11. Describing Angular or Circular Motion Introduction Examples of angular motion occur frequently. Examples include the rotation of a bicycle tire, a merrygoround, a toy top, a food processor, a laboratory
More informationRotational Inertia Demonstrator
WWW.ARBORSCI.COM Rotational Inertia Demonstrator P33545 BACKGROUND: The Rotational Inertia Demonstrator provides an engaging way to investigate many of the principles of angular motion and is intended
More information6.1: Angle Measure in degrees
6.1: Angle Measure in degrees How to measure angles Numbers on protractor = angle measure in degrees 1 full rotation = 360 degrees = 360 half rotation = quarter rotation = 1/8 rotation = 1 = Right angle
More informationPhysics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationNo 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
More informationLecture 16. Newton s Second Law for Rotation. Moment of Inertia. Angular momentum. Cutnell+Johnson: 9.4, 9.6
Lecture 16 Newton s Second Law for Rotation Moment of Inertia Angular momentum Cutnell+Johnson: 9.4, 9.6 Newton s Second Law for Rotation Newton s second law says how a net force causes an acceleration.
More information3600 s 1 h. 24 h 1 day. 1 day
Week 7 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
More informationChapter 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
More informationPHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013
PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be
More informationPHYS 1014M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PHYS 1014M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in
More informationHomework 4. problems: 5.61, 5.67, 6.63, 13.21
Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find
More informationChapter 13, example problems: x (cm) 10.0
Chapter 13, example problems: (13.04) Reading Fig. 1330 (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.
More informationChapter 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...
More informationRotation: 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
More informationTennessee 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 Fgrade. Other instructions will be given in the Hall. MULTIPLE CHOICE.
More informationRotation. Moment of inertia of a rotating body: w I = r 2 dm
Rotation Moment of inertia of a rotating body: w I = r 2 dm Usually reasonably easy to calculate when Body has symmetries Rotation axis goes through Center of mass Exams: All moment of inertia will be
More informationCenter of Gravity. We touched on this briefly in chapter 7! x 2
Center of Gravity We touched on this briefly in chapter 7! x 1 x 2 cm m 1 m 2 This was for what is known as discrete objects. Discrete refers to the fact that the two objects separated and individual.
More informationTorque and Rotary Motion
Torque and Rotary Motion Name Partner Introduction Motion in a circle is a straightforward extension of linear motion. According to the textbook, all you have to do is replace displacement, velocity,
More informationLecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is
Lecture 17 Rotational Dynamics Rotational Kinetic Energy Stress and Strain and Springs Cutnell+Johnson: 9.49.6, 10.110.2 Rotational Dynamics (some more) Last time we saw that the rotational analog of
More informationAP Physics Circular Motion Practice Test B,B,B,A,D,D,C,B,D,B,E,E,E, 14. 6.6m/s, 0.4 N, 1.5 m, 6.3m/s, 15. 12.9 m/s, 22.9 m/s
AP Physics Circular Motion Practice Test B,B,B,A,D,D,C,B,D,B,E,E,E, 14. 6.6m/s, 0.4 N, 1.5 m, 6.3m/s, 15. 12.9 m/s, 22.9 m/s Answer the multiple choice questions (2 Points Each) on this sheet with capital
More informationCentripetal 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 informationLab 7: Rotational Motion
Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME9472), string with loop at one end and small white bead at the other end (125
More informationNEWTON S LAWS OF MOTION
NEWTON S LAWS OF MOTION Background: Aristotle believed that the natural state of motion for objects on the earth was one of rest. In other words, objects needed a force to be kept in motion. Galileo studied
More information356 CHAPTER 12 Bob Daemmrich
Standard 7.3.17: Investigate that an unbalanced force, acting on an object, changes its speed or path of motion or both, and know that if the force always acts toward the same center as the object moves,
More informationTorque and Rotation. Physics
Torque and Rotation Physics Torque Force is the action that creates changes in linear motion. For rotational motion, the same force can cause very different results. A torque is an action that causes objects
More informationSOLID MECHANICS DYNAMICS TUTORIAL MOMENT OF INERTIA. This work covers elements of the following syllabi.
SOLID MECHANICS DYNAMICS TUTOIAL MOMENT OF INETIA This work covers elements of the following syllabi. Parts of the Engineering Council Graduate Diploma Exam D5 Dynamics of Mechanical Systems Parts of the
More informationChapter 4 Dynamics: Newton s Laws of Motion. Copyright 2009 Pearson Education, Inc.
Chapter 4 Dynamics: Newton s Laws of Motion Force Units of Chapter 4 Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal
More informationPHYS 211 FINAL FALL 2004 Form A
1. Two boys with masses of 40 kg and 60 kg are holding onto either end of a 10 m long massless pole which is initially at rest and floating in still water. They pull themselves along the pole toward each
More informationSolution 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
More informationChapter 6 Circular Motion
Chapter 6 Circular Motion 6.1 Introduction... 1 6.2 Cylindrical Coordinate System... 2 6.2.1 Unit Vectors... 3 6.2.2 Infinitesimal Line, Area, and Volume Elements in Cylindrical Coordinates... 4 Example
More informationPhysics 1120: Work & Energy Solutions
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Physics 1120: Work & Energy Solutions Energy 1. In the diagram below, the spring has a force constant of 5000
More information7. Kinetic Energy and Work
Kinetic Energy: 7. Kinetic Energy and Work The kinetic energy of a moving object: k = 1 2 mv 2 Kinetic energy is proportional to the square of the velocity. If the velocity of an object doubles, the kinetic
More informationPhysics 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
More informationwww.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x
Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity
More informationPhysics 201 Homework 8
Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 Nm is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kgm 2. What is the
More informationMECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 2 BELT DRIVES
MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL BELT DRIVES Simple machines: lifting devices e.g. lever systems, inclined plane, screw jack, pulley blocks, Weston differential pulley
More information6: Applications of Newton's Laws
6: Applications of Newton's Laws Friction opposes motion due to surfaces sticking together Kinetic Friction: surfaces are moving relative to each other a.k.a. Sliding Friction Static Friction: surfaces
More informationPractice 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,
More informationBHS Freshman Physics Review. Chapter 2 Linear Motion Physics is the oldest science (astronomy) and the foundation for every other science.
BHS Freshman Physics Review Chapter 2 Linear Motion Physics is the oldest science (astronomy) and the foundation for every other science. Galileo (15641642): 1 st true scientist and 1 st person to use
More informationCh 6 Forces. Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79
Ch 6 Forces Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79 Friction When is friction present in ordinary life?  car brakes  driving around a turn  walking  rubbing your hands together
More information1) The gure below shows the position of a particle (moving along a straight line) as a function of time. Which of the following statements is true?
Physics 2A, Sec C00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to ll your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationPHYSICS 111 HOMEWORK SOLUTION #10. April 10, 2013
PHYSICS 111 HOMEWORK SOLUTION #10 April 10, 013 0.1 Given M = 4 i + j 3 k and N = i j 5 k, calculate the vector product M N. By simply following the rules of the cross product: i i = j j = k k = 0 i j
More informationCopyright 2011 Casa Software Ltd. www.casaxps.com
Table of Contents Variable Forces and Differential Equations... 2 Differential Equations... 3 Second Order Linear Differential Equations with Constant Coefficients... 6 Reduction of Differential Equations
More informationMechanical Principles
Unit 4: Mechanical Principles Unit code: F/601/1450 QCF level: 5 Credit value: 15 OUTCOME 4 POWER TRANSMISSION TUTORIAL 2 BALANCING 4. Dynamics of rotating systems Single and multilink mechanisms: slider
More informationNewton s Laws of Motion
Section 3.2 Newton s Laws of Motion Objectives Analyze relationships between forces and motion Calculate the effects of forces on objects Identify force pairs between objects New Vocabulary Newton s first
More informationPHYSICS 111 HOMEWORK SOLUTION #9. April 5, 2013
PHYSICS 111 HOMEWORK SOLUTION #9 April 5, 2013 0.1 A potter s wheel moves uniformly from rest to an angular speed of 0.16 rev/s in 33 s. Find its angular acceleration in radians per second per second.
More informationPhysics 160 Biomechanics. Angular Kinematics
Physics 160 Biomechanics Angular Kinematics Questions to think about Why do batters slide their hands up the handle of the bat to lay down a bunt but not to drive the ball? Why might an athletic trainer
More information1. Newton s Laws of Motion and their Applications Tutorial 1
1. Newton s Laws of Motion and their Applications Tutorial 1 1.1 On a planet far, far away, an astronaut picks up a rock. The rock has a mass of 5.00 kg, and on this particular planet its weight is 40.0
More informationEXPERIMENT: MOMENT OF INERTIA
OBJECTIVES EXPERIMENT: MOMENT OF INERTIA to 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 as mass plays in
More informationExam 3 Review Questions PHY Exam 3
Exam 3 Review Questions PHY 2425  Exam 3 Section: 8 1 Topic: Conservation of Linear Momentum Type: Numerical 1 An automobile of mass 1300 kg has an initial velocity of 7.20 m/s toward the north and a
More informationMore of Newton s Laws
More of Newton s Laws Announcements: Tutorial Assignments due tomorrow. Pages 1921, 23, 24 (not 22,25) Note Long Answer HW due this week. CAPA due on Friday. Have added together the clicker scores so
More informationTrigonometry 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
More informationPhysics 9 Fall 2009 Homework 7  Solutions
Physics 9 Fall 009 Homework 7  s 1. Chapter 33  Exercise 10. At what distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the loop? Give your answer
More informationCHAPTER 6 WORK AND ENERGY
CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS. REASONING AND SOLUTION The work done by F in moving the box through a displacement s is W = ( F cos 0 ) s= Fs. The work done by F is W = ( F cos θ). s From
More informationRotational 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 informationPhysics 125 Practice Exam #3 Chapters 67 Professor Siegel
Physics 125 Practice Exam #3 Chapters 67 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the
More informationSOLID MECHANICS BALANCING TUTORIAL BALANCING OF ROTATING BODIES
SOLID MECHANICS BALANCING TUTORIAL BALANCING OF ROTATING BODIES This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 4. On completion of this tutorial
More informationC 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
More informationTIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 1111, Exam 3 Section 1 Version 1 December 6, 2005 Total Weight: 100 points
TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 3 Section 1 Version 1 December 6, 2005 Total Weight: 100 points 1. Check your examination for completeness prior to starting.
More informationConceptual Questions: Forces and Newton s Laws
Conceptual Questions: Forces and Newton s Laws 1. An object can have motion only if a net force acts on it. his statement is a. true b. false 2. And the reason for this (refer to previous question) is
More informationF N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26
Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250N force is directed horizontally as shown to push a 29kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,
More informationChapter 7 Homework solutions
Chapter 7 Homework solutions 8 Strategy Use the component form of the definition of center of mass Solution Find the location of the center of mass Find x and y ma xa + mbxb (50 g)(0) + (10 g)(5 cm) x
More informationLab 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
More informationCentripetal force, rotary motion, angular velocity, apparent force.
Related Topics Centripetal force, rotary motion, angular velocity, apparent force. Principle and Task A body with variable mass moves on a circular path with adjustable radius and variable angular velocity.
More informationRotational Kinetic Energy
Objective: The kinetic energy of a rotating disk and falling mass are found; the change in their kinetic energy is compared with the change in potential energy of the falling mass. The conservation of
More informationAP Physics C Fall Final Web Review
Name: Class: _ Date: _ AP Physics C Fall Final Web Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. On a position versus time graph, the slope of
More information3 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
More informationMass, energy, power and time are scalar quantities which do not have direction.
Dynamics Worksheet Answers (a) Answers: A vector quantity has direction while a scalar quantity does not have direction. Answers: (D) Velocity, weight and friction are vector quantities. Note: weight and
More informationPhysics 1401  Exam 2 Chapter 5NNew
Physics 1401  Exam 2 Chapter 5NNew 2. The second hand on a watch has a length of 4.50 mm and makes one revolution in 60.00 s. What is the speed of the end of the second hand as it moves in uniform circular
More informationPhysics 11 Assignment KEY Dynamics Chapters 4 & 5
Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problemsolving questions, draw appropriate free body diagrams and use the aforementioned problemsolving method.. Define the following
More informationChapter 13. Gravitation
Chapter 13 Gravitation 13.2 Newton s Law of Gravitation In vector notation: Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G = 6.67
More information= Ps cos 0 = (150 N)(7.0 m) = J F N. s cos 180 = µ k
Week 5 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions o these problems, various details have been changed, so that the answers will come out dierently. The method to ind the solution
More informationDynamics of Rotational Motion
Chapter 10 Dynamics of Rotational Motion PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 5_31_2012 Goals for Chapter
More informationDownloaded from www.studiestoday.com
Class XI Physics Ch. 4: Motion in a Plane NCERT Solutions Page 85 Question 4.1: State, for each of the following physical quantities, if it is a scalar or a vector: Volume, mass, speed, acceleration, density,
More information1 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
More informationv 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
More informationENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION
ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION This tutorial covers prerequisite material and should be skipped if you are
More informationSolution: 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
More informationFall 12 PHY 122 Homework Solutions #8
Fall 12 PHY 122 Homework Solutions #8 Chapter 27 Problem 22 An electron moves with velocity v= (7.0i  6.0j)10 4 m/s in a magnetic field B= (0.80i + 0.60j)T. Determine the magnitude and direction of the
More information