Solve the Problem

Question

A gear with a radius of 8 centimeters is turning at pi/7 radians per second. What is the linear speed at a point on the outer edge of the gear?

Answer 1

The linear (or tangential) speed of a point on a rotating object is given by

 

v = ω r,

 

where ω is the angular speed (in rad/s = s^-1) and r the distance between the point and the rotational axis. In this case, r is the radius and

 

v = (pi/7) s^-1 (8 cm) = 8pi/7 cm/s.

 

With 1 significant digit, this rounds to 4 cm/s.