A pulley with a radius of 10.0 cm is mounted on an axle that passes through the

Question

A pulley with a radius of 10.0 cm is mounted on an axle that passes through the center of the pulley. The axle allows the pulley to rotate with negligible friction. The pulley is initially at rest. At t-0, you start pulling on the end of a string that is wrapped around the outside of the pulley, giving the pulley a constant angular acceleration of 2.30 rad/s2. After t = 4.00 s of you pulling on the string, calculate the following. (a) the instantaneous angular speed of the pulley rad/s (b) the instantaneous speed of a point on the edge of the pulley m/s (c) the number of revolutions the pulley has made (this does not have to be an integer) revolutions

Explanation / Answer

alpha = 2.30 rad/s^2

t = 4s

and w0 = 0

(A) w = w0 + alpha t

w = 9.2 rad / sec

(B) v = w r = 9.2 x 0.10 = 0.92 m/s

(c) theta = w0 t + alpha t^2 /2

theta = 18.4 rad

revolutions = 18.4/ 2pi = 2.9 rev

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