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Question

A wheel having moment of inertia I=4 kg-m2 about its natural axis is rotating at the rate of ωo=120 rpm. Find the magnitude of constant torque which can stop the wheel in 3 minutes.

A
4π/45 N-m
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B
2π/45 N-m
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C
16π/3 N-m
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D
160 N-m
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Solution

The correct option is A 4π/45 N-m
Given ,
I=4 kg-m2
wo=120 rpm=120×2π60 rad/s
ωo=4π rad/s

Let constant angular acceleration required to stop wheel's rotation is α
then,
As wheel stops,
final angular velocity, ω=0
and given: t=3 min=(3×60) s
w=wo+αt
0=wo+α(3×60)
α=4π3×60 rad/s2

We know,
Torque τ=Iα
=4×4π3×60
=4π45 N-m
Here ve sign indicates torque is opposing the motion of wheel.
|τ|=4π45 N-m

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