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Question

A particle is moving in a circular path with an angular velocity of 2 rad/s and angular acceleration of α=52ω, where ω is the angular velocity at any particular instant. Find the angular velocity after the particle has moved through an angle of 3π.

A
20.64 rad/s
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B
15.52 rad/s
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C
25.56 rad/s
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D
28.25 rad/s
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Solution

The correct option is C 25.56 rad/s
Given angular acceleration is
α=52ω
α=dωdt=52ω

Using chain rule, we get,

dωdθdθdt=52ω

ωdωdθ=52ω

2dω=5 dθ

Integrating with limits on both sides, we get,

2ω2dω=53π0dθ

2(ω2)=5(3π0)

ω=15π+4225.56 rad/s





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