A wheel starts rotating from rest at time t = 0 with a angular acceleration of 50 radians / s 2 . The angular acceleration ( α ) decreases to zero value after 5 seconds. During this interval, α varies

Question

A wheel starts rotating from rest at time t = 0 with a angular acceleration of 50 radians / s 2 . The angular acceleration ( α ) decreases to zero value after 5 seconds. During this interval, α varies according to the equation α = α 0 ​ ( 1 − 5 t ​ ) The angular velocity at t = 5 s will be

TestHub · Accepted Answer

α = α 0 ​ ( 1 − 5 t ​ ) At t = 0 , α = α 0 ​ ∴ α 0 ​ = 50 rad / s 2 d t d ω ​ = α 0 ​ ( 1 − 5 t ​ ) ​ ∴ ∫ 0 ω ​ d ω = α 0 ​ ∫ 0 5 ​ ( 1 − 5 t ​ ) d t ⇒ ω = α 0 ​ [ t − 10 t 2 ​ ] 0 5 ​ = 50 ( 5 − 10 25 ​ ) rad / s = 125 rad / s ​

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