A pulley of radius 2 m is rotated about its axis by a force F = ( 20 t − 5 t 2 ) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of

Question

A pulley of radius 2 m is rotated about its axis by a force F = ( 20 t − 5 t 2 ) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation made by the pulley before its direction of motion if reversed, is :

TestHub · Accepted Answer

r × F = l × α 2 ( 20 t − 5 t 2 ) = 10 α ⇒ α = 4 t − t 2 dt d ω ​ = 4 t − t 2 d ω = ( 4 t 2 − t 2 ) dt ω = 2 t 2 − 3 t 3 ​ (on integration) ω = 0 ⇒ t = 6 s

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