A circular disk of radius 3.88 m and mass 181 kg has a cord attach to its circum

Question

A circular disk of radius 3.88 m and mass 181 kg has a cord attach to its circumference edge.
A force of 812 N is applied to this cord in a tangential direction to the disk which causes the
disk to start spinning from rest. This force is applied for a total of 2.88 s and after this time,
the disk continues to rotate at a constant angular speed. (a) What is the moment of inertia of
this disk? (b) What is the angular speed of the disk at 2.88 seconds? (c) How many revolutions
will the disk make in 20.0 seconds? (d) What is the rotational kinetic energy of this disk at the
20.0 second mark? (Note that I =
1
2
MR
2
for a disk spinning about its center. (Ignore friction

in the bearings).

Explanation / Answer

a] I = 0.5 mr^2 = 0.5*181*3.88^2 = 1362 kgm^2

b] Angular speed w = alpha*t = [torque/i]*t = [812*3.88/1362]*2.88 = 6.662 rad/s

c] We are assuming that it has asked in next 20s, not including the 2.88s.

revolutions = 6.662*20/2pi = 21.2 revolutions

d] KE = 0.5iw^2 = 0.5*1362*6.662^2 = 30224 J

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