FIGURE 10-3
-Fig. 10-3 illustrates a simplified roller bearing. The inner cylinder has a radius of 1.0 cm and is stationary. The outer hollow cylinder has a radius of 1.2 cm and is rotating at 8.0 rpm. Between the two cylinders are several small cylinders with a radius of 0.10 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. What is the angular speed of the small cylinders?
A)12 rpm
B)10 rpm
C)48 rpm
D)36 rpm
E)50 rpm

Question

FIGURE 10-3 
-Fig. 10-3 illustrates a simplified roller bearing. The inner cylinder has a radius of 1.0 cm and is stationary. The outer hollow cylinder has a radius of 1.2 cm and is rotating at 8.0 rpm. Between the two cylinders are several small cylinders with a radius of 0.10 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. What is the angular speed of the small cylinders?
A)12 rpm 
B)10 rpm 
C)48 rpm 
D)36 rpm 
E)50 rpm

Quizplus · Accepted Answer

The small cylinders roll without slipping, meaning the linear speed at the contact point with both the inner and outer cylinders is the same. The outer cylinder's linear speed is 1.2 cm * 8.0 rpm = 9.6 cm/min. The small cylinders have a radius of 0.10 cm, so their angular speed is 9.6 cm/min / 0.10 cm = 96 rpm. However, they rotate in the opposite direction to the outer cylinder, so the net angular speed is 96 rpm / 2 = 48 rpm.

FIGURE 10-3 -Fig. 10-3 Illustrates a Simplified Roller Bearing. the Inner Cylinder