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Question

The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t)=3t39t2 (Here t is in seconds). The angular acceleration of the wheel becomes zero at

A
t=1 s
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B
t=0.5 s
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C
t=0.25 s
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D
t=2 s
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Solution

The correct option is A t=1 s
We know that angular velocity is the rate of change of angular position of a rotating body and angular acceleration refers to the rate of change of angular velocity

It is given that θ(t)=3t39t2

hence,
ω=dθdt=9t218t
α=d2θdt2=dωdt=18t18
It is said that angular acceleration becomes 0, hence
α=18t18=0
t=1 s

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