Physics 103: Lecture 12 Rotational Kinematics

1. Physics 103: Lecture 12Rotational Kinematics • Today’s lecture will cover • rotational kinematics • centripetal force Physics 103 - Spring 2003-04

2. s q = R Dq Dw w = a = Dt Dt Rotation s q R Physics 103 - Spring 2003-04

3. Vector Nature of Angular Quantities • Right hand rule • Grasp the axis of rotation with your right hand • Wrap your fingers in the direction of rotation • Your thumb points in the direction of w Physics 103 - Spring 2003-04

4. V2 V1 V1 DV V2 Centripetal Acceleration Force is required to change motion i.e. velocity (magnitude and direction) magnitude is constant, but direction changes DV points toward the center of rotation Centrifugal force? Physics 103 - Spring 2003-04

5. Centripetal Acceleration Physics 103 - Spring 2003-04

6. And for a point at a distance R from the rotation axis: • x = Rv = R a = R Rotation Summary (with comparison to 1-D kinematics) Angular Linear Physics 103 - Spring 2003-04

7. Total Acceleration • The tangential component of the acceleration is due to changing speed • The centripetal component of the acceleration is due to changing direction • Total acceleration can be found from these components Physics 103 - Spring 2003-04

8. CORRECT Lecture 13,Preflight 1 & 2 You and a friend are playing on the merry-go-round at Carle Park. You stand at the outer edge of the merry-go-round and your friend stands halfway between the outer edge and the center. Assume the rotation rate of the merry-go-round is constant. Who has the greatest angular velocity? 1. You do2. Your friend does3. Same You both cover the same angle in the same amount of time. Physics 103 - Spring 2003-04

9. CORRECT Lecture 13,Preflight 3 & 4 Who has the greatest tangential velocity? 1. You do2. Your friend does3. Same for a given angular speed, the tangential speed is directly proportional to the radius Physics 103 - Spring 2003-04

10. CORRECT Lecture 13,Preflight 5 & 6 Who has the greatest centripetal acceleration? 1. You do2. Your friend does3. Same centripetal acceleration = rw2 - you have a larger radius so therefore you have a larger centripetal acceleration Physics 103 - Spring 2003-04

11. Your Car Your Friends Car Physics 103 - Spring 2003-04

12. CORRECT Lecture 13,Preflight 7 & 8 Tired of playing in the park, you and your friend hop into your cars and decide to drive over to Michael’s Frozen Custard. During some part of your trip down Monroe Street your cars are side by side and have the same speed and the same acceleration. The wheels on your 1965 Corvette Stingray have a larger radius than the wheels on your friends 1986 Chevette Hatchback. Which car's wheels have the greatest angular acceleration? 1. Corvette2. Chevette 3. Same The Chevette's wheels have a smaller circumference than the Corvette's wheels therefore the wheels of the Chevette must make more rotations to keep up. Physics 103 - Spring 2003-04

13. Forces Causing Centripetal Acceleration • Newton’s Second Law says that the centripetal acceleration is accompanied by a force • F = maC • F stands for any force that keeps an object following a circular path • Tension in a string • Gravity • Force of friction Physics 103 - Spring 2003-04

14. Problem Solving Strategy • Draw a free body diagram, showing and labeling all the forces acting on the object(s) • Choose a coordinate system that has one axis perpendicular to the circular path and the other axis tangent to the circular path • Find the net force toward the center of the circular path (this is the force that causes the centripetal acceleration) • Solve as in Newton’s second law problems • The directions will be radial and tangential • The acceleration will be the centripetal acceleration Physics 103 - Spring 2003-04

15. Applications of Forces Causing Centripetal Acceleration • Many specific situations will use forces that cause centripetal acceleration • Level curves • Banked curves • Horizontal circles • Vertical circles Physics 103 - Spring 2003-04

16. Level Curves • Friction is the force that produces the centripetal acceleration • Can find the frictional force, µ, v Physics 103 - Spring 2003-04

17. Banked Curves • A component of the normal force adds to the frictional force to allow higher speeds • Can the ability of car to turn be made independent of the coefficient of friction? • Yes • No Physics 103 - Spring 2003-04

18. V2 g tan q = R Example • An automobile successfully turns on a very icy roadway (no friction). This means that the net external force is just what is needed to provide the centripetal acceleration. Note that there is no dependence on m,(which is good since it is zero!! ) Physics 103 - Spring 2003-04

19. Horizontal Circle • The horizontal component of the tension causes the centripetal acceleration Physics 103 - Spring 2003-04

20. Vertical Circle • Look at the forces at the top of the circle • The minimum speed at the top of the circle can be found • Should we be worried about the mass of the people on the roller coaster? • Yes • No Physics 103 - Spring 2003-04

21. And for a point at a distance R from the rotation axis: • x = Rv = R a = R Rotation Summary (with comparison to 1-D kinematics) Angular Linear Physics 103 - Spring 2003-04