AP Physics C Mechanics 2.7: Kinetic Friction

A uniform disk and ring, each of mass M and radius R, roll without slipping along a horizontal

surface, as shown in Figure 1. The outer edges of the disk and ring are made of the same

material. The center of mass of the disk and the center of mass of the ring each initially move

with the same constant speed v.

The disk and the ring then smoothly transition to a ramp that is inclined at an angle $\theta$ above

the horizontal. Both the disk and the ring continue to roll without slipping as they move up the

ramp, as shown in Figure 2.

The ring travels a greater distance along the ramp than the disk travels before each

momentarily comes to rest.

In a different scenario, the centers of mass of the original disk and ring each have the same

initial speed v as they did in the original scenario. The ramp is replaced by a new ramp on

which the disk and the ring initially slip as they roll up the new ramp.

Indicate whether the magnitude of the kinetic frictional force exerted on the disk by the

new ramp is greater than, less than, or equal to the magnitude of the kinetic frictional force

exerted on the ring by the new ramp while both are slipping.

Briefly justify your answer.