A uniformdensity wheel of mass 11 kg and radius 040 m rotate

A uniform-density wheel of mass 11 kg and radius 0.40 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 12 N for 0.90 s.

(a) What is the final angular speed?
_f = ?????? radians/s

(b) What was the average angular speed?
_average = ??????radians/s

(c) Through how big an angle did the wheel turn?
= ??????? radians

(d) How much string came off the wheel?
d = ??????? m

Solution

a) I_w,f = I_w,i + RF_t = RF_t / I

= w_f + w_i

= (2 * 0.40 * 12 * 0.90) / (11 * 0.40² )

= 4.91 rad/sec

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b) w_avg = (w_i + w_f) / 2

= 4.91 / 2

= 2.46 rad/sec

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c) Theta = w_avg * change in time = 2.46 * 0.90

= 2.21 rad

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d) d = R * Theta

= 2.21 * 0.40

= 0.886 m