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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/sGiven angular acceleration is α=52ω ⇒α=dωdt=52ω Using chain rule, we get, dωdθ⋅dθdt=52ω ⇒ω⋅dωdθ=52ω ⇒2⋅dω=5 dθ Integrating with limits on both sides, we get, 2∫ω2dω=5∫3π0dθ ⇒2(ω−2)=5(3π−0) ⇒ω=15π+42≈25.56 rad/s

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