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Question

The speed of a particle travelling in a circle of radius 20 cm increases uniformly from 6 m/s to 8 m/s in 4 sec. The angular acceleration of particle is :

A
5 rad/ s2
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B
7.5 rad/ s2
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C
2.5 rad/ s2
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D
2 rad/ s2
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Solution

The correct option is C 2.5 rad/ s2
Since speed increases uniformly, average tangential acceleration will be equal to instantaneous tangential acceleration.

Therefore, instantaneous tangential acceleration is given by,

at=dvdt=v2v1t2t1

at=864=0.5 m/s2

Angular acceleration of the particle will be,

α=atr

α=0.5 m/s2(20100 m)

α=52=2.5 rad/s2

Alternatve:

α=ωtωot=vurt

α=860.2×4=20.8=2.5 rad/s2
Why this question ?
It intends to your understanding of fundamentals of average and instantaneous tangential acceleration in a circular motion.
Tip: In case of uniform circular motion the average and instantaneous value of tangential acceleration will be the same.

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