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Question

A thin uniform solid wheel is initially rotating with an angular velocity 50 rad/s. The mass of the wheel is given to be 4 kg and the radius of the wheel is 1 m. If the wheel comes to rest in 10 s, find the magnitude of the average retarding torque acting on the wheel (in N-m)
(Assume uniform angular retardation)

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Solution

Given, initial angular velocity of wheel (ω)=50 rad/s
Mass of the wheel M=4 kg
Radius of the wheel R=1 m
Moment of inertial of solid disc (wheel) about axis of rotation
I=MR22=2 kg m2

After 10 s, wheel comes to rest
Applying ω=ω0+αt, we get
0=50αt
or |α|=5 rad/s2
Thus, magnitude of average retarding torque acting on the wheel is
|τ|=Iα
=2×5=10 N-m

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