Radial & Tangential Acceleration for Non Uniform Circular Motion
The angular v...
Question
The angular velocity of a particle moving along positive direction varies as ω=β√θ (in rad/s) where β is a positive constant. Assuming that θ=0 (at time t=0), the value of angular acceleration of the particle
A
Is directly proportional to time
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B
Is constant with time
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C
Is inversely proportional with time
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D
Cannot be determined as data is insufficient
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Solution
The correct option is B Is constant with time Given, Angular velocity, ω=β√θ ⇒dθdt=β√θ dθ√θ=βdt
Integrating on both sides, ∫θ0dθ√θ=∫t0βdt 2√θ=βt ∴θ=β2t24 ⇒dθdt=2β2t4=β2t2
Then, angular acceleration α=d2θdt2=β22 ∴ Angular acceleration is constant