In a part of a printing press, a roller with a radius of 10 cm, rolls without slipping on the outside of a fixed cylinder with a radius of 30 cm. There is a connecting rod that connects the center of the cylinder to the axle of the roller. If the angular speed of the roller is 60 rad/s, what is the angular speed of the connecting rod?
A) 15 rad/s
B) 20 rad/s
C) 120 rad/s
D) 150 rad/s
E) 180 rad/s

Question

Quizplus · Accepted Answer

First, we need to find the linear speed of the roller by using the formula: 
v = ωr 
where ω is the angular speed in radians per second, and r is the radius in meters.

v = (60 rad/s)(0.1 m) = 6 m/s

Next, we can use the fact that the roller is rolling without slipping to relate the linear speeds of the roller and the cylinder:

v_roller = v_cylinder

ω_roller r_roller = ω_cylinder r_cylinder

ω_cylinder = (ω_roller r_roller) / r_cylinder

ω_cylinder = (60 rad/s)(0.1 m) / 0.3 m = 20 rad/s

Therefore, the angular speed of the connecting rod is also 20 rad/s (since it is connected to the center of the cylinder).

The correct answer is B.

In a Part of a Printing Press, a Roller with a Radius