Question
The angular velocity of a flywheel changes with time as ω = a - bt where a and b are constants.
Prove that the angle through which it rotates before coming to rest is a^2/2b.
The angular velocity of a flywheel changes with time as ω = a - bt where a and b are constants.
Prove that the angle through which it rotates before coming to rest is a^2/2b.
Answer
ω = a - bt
at t = 0, initial angular velocity, ωo = a
angular acceleration,
α = dω/dt = - b
When it comes to rest, ω = 0
=> ω^2 - ωo^2 = 2αθ, where θ = angular displacement before coming to rest
=> angular displacement, θ
= (ω^2 - ωo^2) / 2α
= (0 - a^2) / [2*(-b)]
= a^2/2b.
ω = a - bt
at t = 0, initial angular velocity, ωo = a
angular acceleration,
α = dω/dt = - b
When it comes to rest, ω = 0
=> ω^2 - ωo^2 = 2αθ, where θ = angular displacement before coming to rest
=> angular displacement, θ
= (ω^2 - ωo^2) / 2α
= (0 - a^2) / [2*(-b)]
= a^2/2b.
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