A particle at rest starts moving with a constant angular acceleration of 4 rad / s 2 in a circular path. The time at which magnitudes of its centripetal acceleration and tangential acceleration will b

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A particle at rest starts moving with a constant angular acceleration of 4 rad / s 2 in a circular path. The time at which magnitudes of its centripetal acceleration and tangential acceleration will be equal, is (in second)

TestHub · Accepted Answer

Initial angular velocity, ω 0 ​ = 0 Angular acceleration, α = 4 Angular velocity at time t , ω = ω 0 ​ + α t = 4 t Tangential acceleration, a t ​ = r α Centripetal acceleration, a c ​ = ω 2 r Given a c ​ = a t ​ ω 2 r = r α ω 2 = α ( 4 t ) 2 = 4 16 t 2 = 4 t 2 = 4 1 ​ t = 2 1 ​ Answer: 2 1 ​

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