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A pulley of radius 2m is rotated about its axis by a force F = (20t – 5t2) newton (wheret is measured in seconds) applied tangentially. If the moment of inertia of the pulley aboutits axis of rotation is 10kgm2, the number of rotations made by the pulley before its directionof motion if reversed is?

A pulley of radius 2m is rotated about its axis by a force F = (20t – 5t2) newton (wheret is measured in seconds) applied tangentially. If the moment of inertia of the pulley aboutits axis of rotation is 10kgm2, the number of rotations made by the pulley before its directionof motion if reversed is?

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1 Answers

Aryan
11 Points
3 years ago
Torque=fR=2f=40t-10t²=10alpha As, Torque=I.alphaAlpha = 4t-t²Omega = alpha. dt=(4t-t²)dt =2t²-t³/3When it stops rotating Omega = 0So, 2t²-t³/3=0t=6secondsTheta (angular displacement) =omega.dt[2t³/3 - t*4/12] limits from 0 to 6=36No. Of revolutions = 36/2pie

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