A block sits on a turntable; we look down on it from above. The turntable starts

Question

A block sits on a turntable; we look down on it from above. The turntable starts at rest, so at time
t = 0 s the block is at = 0 rad and the angular velocity is = 0 rad/s. The turntable rotates with
constant angular acceleration = 0.50 rad/s2. The mass of the block is 1.0 kg, and the block is 0.10
m from the center of the turntable. The radius of the turntable is 0.20 m.
a) At t = 3 s, what is the angular position of the block?
b) How long does it take before the tangential velocity of the block is 0.1 m/s?

Explanation / Answer

(A) angular position, theta = w0 t + alpha t^2 /2

theta = 0 + (0.50)(3^2)/2

= 2.25 rad

(B) v = w r

0.1 = w (0.10)

w = 1 rad/s

w = w0 + alpha t

1 = 0 + 0.50 t

t = 2 sec ......Ans

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