1. CHS Physics Rolling Motion

2. 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.

3. 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

4. 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.

5. 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.

6. Mathematical Model

7. 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.

8. 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.

9. 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.

10. 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.