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Question

If angular position of a particle θ depends on time t as θ=2t2+3, find the average angular velocity at the end of 3 sec and instantaneous angular velocity at t=3 sec (in rad/s)

A
6,12
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B
6,6
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C
8,12
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D
12,4
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Solution

The correct option is A 6,12
We know that,
ωavg=Total angular displacementTotal time
or, ωavg=θfinalθinitialt2t1

We have from the question
θ=2t2+3
θfinal=2(3)2+3=21 rad and
θinitial=2(0)+3=3 rad

Thus, ωavg=21330=6 rad/s

Also, ωinstantaneous=dθdt=d(2t2+3)dt=4t
Thus, at t=3 s,ωinstantaneous=4×3=12 rad/sec.

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