CHS Physics Rolling Motion. A Rolling Wheel Consider three points on a rolling wheel. Consider three points on a rolling wheel. The Center of MassThe.

Slides:

Advertisements

Similar presentations

Chapter 11 Angular Momentum; General Rotation

Advertisements

8.4 Angular Variables and Tangential Variables

Chapter 11 Angular Momentum

Angular Momentum The vector angular momentum of the point mass m about the point P is given by: The position vector of the mass m relative to the point.

Rotational Motion Chapter Opener. Caption: You too can experience rapid rotation—if your stomach can take the high angular velocity and centripetal acceleration.

Chapter 8 Rotational kinematics

Physics 111: Lecture 19, Pg 1 Physics 111: Lecture 19 Today’s Agenda l Review l Many body dynamics l Weight and massive pulley l Rolling and sliding examples.

Rotational Motion.

Physics: Principles with Applications, 6th edition

Rolling, Torque, and Angular Momentum

Chapter 10 Rotational Motion and Torque Angular Position, Velocity and Acceleration For a rigid rotating object a point P will rotate in a circle.

Chapter 8: Rotational Kinematics Lecture Notes

Chapter 10 Rotational Motion

Halliday/Resnick/Walker Fundamentals of Physics

Physics. Session Rotational Mechanics - 5 Session Objectives.

Work Let us examine the work done by a torque applied to a system. This is a small amount of the total work done by a torque to move an object a small.

Rolling. Rolling Condition – must hold for an object to roll without slipping.

Rotation and angular momentum

Rigid Body: Rotational and Translational Motion; Rolling without Slipping 8.01 W11D1 Today’s Reading Assignment Young and Freedman: 10.3.

CHAPTER 11 : ROLLING MOTION AND ANGULAR MOMENTUM

Chapters 10, 11 Rotation and angular momentum. Rotation of a rigid body We consider rotational motion of a rigid body about a fixed axis Rigid body rotates.

Rolling, Torque, and Angular Momentum

3-Dimensional Rotation: Gyroscopes

Chapter 10 Rotation.

Example Problem The parallel axis theorem provides a useful way to calculate I about an arbitrary axis. The theorem states that I = Icm + Mh2, where Icm.

Rotational Kinematics Chapter 8. Expectations After Chapter 8, students will:  understand and apply the rotational versions of the kinematic equations.

1 Rotational Kinematics Chapter 9 October 11, 2005 Today’s Topics Translation vs. rotation Variables used for rotation: , ,  Four angular equations.

Circular Motion Topics Angular Measure Angular Speed and Velocity Uniform Circular Motion and Centripetal Acceleration Angular Acceleration.

Rotational Kinematics. Angular Position Degrees and revolutions: Angular Position θ > 0 θ < 0.

How do you relate the angular acceleration of the object to the linear acceleration of a particular point? There are actually two perpendicular components.

今日課程內容 CH10 轉動角位移、角速度、角加速度等角加速度運動力矩轉動牛頓第二運動定律轉動動能轉動慣量.

Chapter 8 Rotational Motion.

 When an extended object, like a wheel, rotates about its axis, the motion cannot be analyzed by treating the object as a particle because at any given.

Distance, Displacement and Speed 3/25/2011. What do you need in order to know that something is moving?  A FRAME OF REFERENCE!  A system of objects.

Rotational and Translational Motion Dynamics 8

Motion Cristinebi F. Abanador Jana Marie P. Mancenido ABMCJ-2A.

AP Physics C Montwood High School R. Casao. When a wheel moves along a straight track, the center of the wheel moves forward in pure translation. A point.

Rolling, torque, and angular momentum

今日課程內容 CH10 轉動角位移、角速度、角加速度等角加速度運動轉動與移動關係轉動動能轉動慣量力矩轉動牛頓第二運動定律.

 If disk angular velocity changes (  is not constant), then we have an angular acceleration   For some point on the disk  From the definition of translational.

Physics Section 7.1 Define and apply circular motion What is circular motion? Any object that revolves about.

R. Field 2/5/2013 University of Florida PHY 2053Page 1 Circular Motion: Angular Variables The arc length s is related to the angle  (in radians = rad)

Angular Displacement, Velocity, and Acceleration Rotational Energy Moment of Inertia Torque Work, Power and Energy in Rotational Motion.

CHAPTER 8 Rotational Kinematics. Go to this page on your laptop or computer: ◦ ms/Labs/ClassicCircularForceLab/index.html.

Rotational Motion – Part I AP Physics C. The radian  There are 2 types of pure unmixed motion:  Translational - linear motion  Rotational - motion.

Perfect Rolling (no sliding!) Consider a disk rolling without slipping with a Uniform Acceleration. While most points both rotate and move linearly, the.

Physics 211 Rolling Motion of a Rigid Body Vector Product and Torque Angular Momentum Rotation of a Rigid Body about a Fixed Axis Conservation of Angular.

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

Chapter 10 Lecture 18: Rotation of a Rigid Object about a Fixed Axis: II.

Rigid Body: Rotational and Translational Motion; Rolling without Slipping 8.01 W11D1.

PHY 151: Lecture 4B 4.4 Particle in Uniform Circular Motion 4.5 Relative Velocity.

Rotational Motion.

Chapter 8 Rotational Motion

Rotational Motion.

Rotational Motion.

Chapter 8 Rotational Motion

PHY131H1F - Class 17 Today: Finishing Chapter 10:

Figure 10.16 A particle rotating in a circle under the influence of a tangential force Ft. A force Fr in the radial direction also must be present to.

Physics: Principles with Applications, 6th edition

Chapter 8 Rotational Motion.

Distance and Displacement

Chapter 11 Rolling, Torque, and Angular Momentum

Physics: Principles with Applications, 6th edition

Chapter 11 Angular Momentum

Rotational Motion Let’s begin with Rotational Kinematics!!

Chapter 8 Rotational Motion

Rigid Body: Rotational and Translational Motion; Rolling without Slipping 8.01 W11D1 Today’s Reading Assignment Young and Freedman: 10.3.

Rolling Motion We may also consider rolling motion at any given instant to be a pure rotation at rate w about the point of contact of the rolling object.

Distance and Displacement

Rigid Body: Rotational and Translational Motion; Rolling without Slipping 8.01 W11D1 Today’s Reading Assignment Young and Freedman:

Presentation transcript:

CHS Physics Rolling Motion

A Rolling Wheel Consider three points on a rolling wheel. Consider three points on a rolling wheel. The Center of MassThe Center of Mass A point on the rimA point on the rim The Center of Mass moves in a straight line. The Center of Mass moves in a straight line. The point on the rim follows semi- circles from the combination of rotation and translation. The point on the rim follows semi- circles from the combination of rotation and translation.

Rolling at Constant Speed Consider a frame of reference that is stationary with respect to the surface. Consider a frame of reference that is stationary with respect to the surface. The COM moves in a straight line with speed v com The COM moves in a straight line with speed v com The point of contact with the surface also has speed v com The point of contact with the surface also has speed v com

A Rolling Wheel Consider a frame of reference that is stationary with respect to the wheel. Consider a frame of reference that is stationary with respect to the wheel. The wheel is simply rotating. The wheel is simply rotating. The COM is stationary. The COM is stationary.

Describing The Motion A person at rest with respect to the surface will see the axle move a distance s during time t. A person at rest with respect to the surface will see the axle move a distance s during time t. A person at rest with respect to the wheel will see the wheel rotate through an angle . A person at rest with respect to the wheel will see the wheel rotate through an angle . The point of the wheel in contact with the surface at time t 0 will move through an arc length of s. The point of the wheel in contact with the surface at time t 0 will move through an arc length of s.

Mathematical Model

Purely Rotational Motion Consider three points on the wheel from the frame at rest with the wheel. Consider three points on the wheel from the frame at rest with the wheel. The COM is stationary. The COM is stationary. The speed of the bottom of the wheel is –v com. The speed of the bottom of the wheel is –v com. The speed of the top of the wheel is v com. The speed of the top of the wheel is v com.

Purely Translational Motion Consider the same three points from a frame that is at rest with respect to the surface. Consider the same three points from a frame that is at rest with respect to the surface. All three points are moving with the same speed, v com, along parallel straight lines. All three points are moving with the same speed, v com, along parallel straight lines.

Combine the Two Descriptions To combine the two descriptions we simply add the velocities at each point. To combine the two descriptions we simply add the velocities at each point. We see that the COM moves with speed v com. We see that the COM moves with speed v com. The bottom of the wheel has speed v=0. The bottom of the wheel has speed v=0. The top of the wheel has speed v=2v com. The top of the wheel has speed v=2v com. Figure 12-4, page 247. Figure 12-4, page 247.

Rotation Only The combination method can be verified by considering the wheel to be rotating only about an axis attached to the contact point. The combination method can be verified by considering the wheel to be rotating only about an axis attached to the contact point. The axis moves along the surface with the object. The axis moves along the surface with the object. Figure 12-5, page 247 Figure 12-5, page 247 The velocity vector at each point is the resultant vector for the translational and tangential velocities. The velocity vector at each point is the resultant vector for the translational and tangential velocities.