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?
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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.