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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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Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
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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.