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Question

A wheel having moment of inertia (I=2 kg-m2) is rotating about its natural axis. The instantaneous angular velocity of a point on a rotating wheel is given by the equation ω(t)=(2t2+4) rad/s. Find the torque acting on wheel about its axis of rotation at t=2 s.

A
14 Nm
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B
12 Nm
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C
10 Nm
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D
16 Nm
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Solution

The correct option is D 16 Nm
Given:
ω(t)=2t2+4
We know that,
α=dωdt
α(t)=ddt(2t2+4)=4t
α|(t=2s)=4×2=8 rad/s2
Again,
τ=Iα
(Given: I=2 kg-m2)
τ=2×8
τ=16 Nm
option (d) is correct.

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