Rotation with Constant Angular Acceleration?

Question

A flywheel turns through 30 rev as it slows from an angular speed of 3.2 rad/s to a stop.
(a) Assuming a constant angular acceleration, find the time for it to come to rest.
in s
(b) What is its angular acceleration?
in rad/s2
(c) How much time is required for it to complete the first 15 of the 30 revolutions?
in s

Answer 1

1 rev=2*π rad
30 rev=188.4 rad

using the equations of motion
188.4=3.2*t-.5*α*t^2
and
0=3.2-α*t
solve for t


a) t=117.75 seconds

b) α=0.027 rad/s^2

c)
94.2=3.2*t-.5*0.027*t^2

solve for t
t=34.5 seconds

BTW: The reason there are two roots is because the displacement equation assumes the wheel stops and then reverses itself, so at 201 seconds the displacement has been reduced to 94.2 rad.

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