1. Rolling

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

3. Rolling One way to view rolling is as a combination of pure rotation and pure translation. Pure Rotation Pure Translation Rolling The point that is in contact with the ground is not in motion with respect to the ground!

4. Rolling The point that is in contact with the ground is not in motion with respect to the ground! Since the bottom point is at rest with respect to the ground, static friction applies if any friction exists at all. Static friction does not dissipate energy. However, there usually is rolling friction caused by the deformation of the object and surface as well as the loss of pieces of the object. Rolling friction does dissipate energy.

5. Rolling If the disk is moving at constant speed, there is no tendency to slip at the contact point and so there is no frictional force. If, however, a force acts on the disk, like when you push on a bike pedal, then there is a tendency to slide at the point of contact so a frictional force acts at that point to oppose that tendency.

6. Rolling Just as rolling motion can be viewed as a combination of pure rotation and pure translation, the kinetic energy of a rolling object can be viewed as a combination of pure rotational kinetic energy and pure translational kinetic energy. Pure Rotation Pure Translation

7. Rolling a.What is the kinetic energy of the hoop? But Note: the v in the E k equation is v cm

8. Rolling a.What is the kinetic energy of the hoop?

9. Rolling b.What percentage of the kinetic energy is associated with rotation and what percentage with translation?

10. Rolling But

11. Rolling

12. 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using dynamics (Newton’s Laws), what is the acceleration of the center of mass of each object as it rolls down the incline?

13. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using dynamics (Newton’s Laws), what is the acceleration of the center of mass of each object as it rolls down the incline? F N and F g exert no torque since they act through the axis of rotation (cm) But

14. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using dynamics (Newton’s Laws), what is the acceleration of the center of mass of each object as it rolls down the incline?

15. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using dynamics (Newton’s Laws), what is the acceleration of the center of mass of each object as it rolls down the incline? But

16. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using dynamics (Newton’s Laws), what is the acceleration of the center of mass of each object as it rolls down the incline?

17. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. b.In what order would the hoop, disk, and sphere reach the bottom of the incline?

18. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using energy principles, what is the velocity of the center of mass of each object as it reaches the bottom of the incline?

19. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using energy principles, what is the velocity of the center of mass of each object as it reaches the bottom of the incline? But

20. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using energy principles, what is the velocity of the center of mass of each object as it reaches the bottom of the incline?

21. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using energy principles, what is the velocity of the center of mass of each object as it reaches the bottom of the incline?

22. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using energy principles, what is the velocity of the center of mass of each object as it reaches the bottom of the incline? But

23. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. a.Using energy principles, what is the velocity of the center of mass of each object as it reaches the bottom of the incline?

24. Rolling 2.A hoop, a disk, and a solid sphere with identical masses and radii roll down an incline of length 2.4 m and angle 35º. b.In what order would the hoop, disk, and sphere reach the bottom of the incline?