FIGURE 10-2
-Figure 10-2 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 10 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) 60 rpm
D) 36 rpm
E) 50 rpm

Question

FIGURE 10-2 
-Figure 10-2 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 10 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) 60 rpm 
D) 36 rpm 
E) 50 rpm

Quizplus · Accepted Answer

The small cylinders roll without slipping, so their linear speed at the point of contact with both the inner and outer cylinders must be the same. The outer cylinder's linear speed is 2π(1.2 cm)(10 rpm) = 24π cm/min. The small cylinders have a radius of 0.10 cm, so their angular speed is (24π cm/min) / (0.10 cm) = 240 rpm. However, since they are in contact with both cylinders, the effective angular speed is half of this, 120 rpm, but relative to the stationary inner cylinder, it is 60 rpm.

FIGURE 10-2 -Figure 10-2 Illustrates a Simplified Roller Bearing. the Inner Cylinder