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?

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 andv = (pi/7) s

^{-1}(8 cm) = 8pi/7 cm/s.With 1 significant digit, this rounds to 4 cm/s.