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Question:

A wheel starts rotating from rest at time t=0 with an angular acceleration of 50 radians/s². The angular acceleration (α) decreases to zero value after 5 seconds. During this interval, α varies according to the equation α = α₀(1 - t/5). The angular velocity at T=5s will be?

10 rad/s

250 rad/s

125 rad/s

100 rad/s

Solution:

α = α₀(1 - t/5)
At t=0, α = α₀ ∴ α₀ = 50 rad/s²
dω/dt = α₀(1 - t/5) ∴ ∫ω₀dω = α₀∫₀⁵(1 - t/5)dt
⇒ ω = α₀[t - t²/10]₀⁵ = 50(5 - 5²/10) rad/s = 125 rad/s.