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Question

if angular velocity of a disc depends an angle rotated THITA as OMEGA =thita sq. + 2thita , then its angular acceleration alpha at thita = 1 is

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Solution

Given, angular velocity, ω =d θdt = θ2 + 2 θ where, θ is angular displacementSince, angular acceleration, α = d ωd t = d ωd θ d θd tα = d ωd θ ωα = dd θ θ2 + 2 θ θ2 + 2 θα = 2 θ + 2 θ2 + 2 θα = 2 θ3 + 6 θ2 + 4 θPutting θ = 1 in above equation, we get α = 12 rad s-2

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