A pulley of radius $$2m$$ is rotated about its axis by a force $$F=20t-5t2$$ newton [where t is measured in $$second)$$ applied tangentially. If the moment of Inertia of the pulley about its axis of rotation is $$10kg-$$ $$m2$$.The number of rotations made by the pulley before its direction of motion reversed is

Question

A pulley of radius   $$2m$$ is rotated about its axis by a force $$F=20t-5t2$$  newton [where t is measured in $$second)$$ applied tangentially. If the moment of Inertia of the pulley about its axis of rotation is $$10kg-$$ $$m2$$.The number of rotations made by the pulley before its direction of motion reversed is

Infinity Learn · Accepted Answer

$$F=20t$$−$$5t2$$ ⇒α$$=FRI=(20t$$−$$5t2)210=4t$$−$$t2$$ ⇒dω$$dt=4t$$−$$t2$$ ⇒∫ ω$$0d$$ω$$=$$∫$$0t(4t$$−$$t2)$$   dt ⇒ω$$=4t22$$−$$t33=2t2$$−$$t33$$ ∴[ω$$=0$$ at $$t=0$$ or $$6s$$] ⇒∫ θ$$0d$$θ$$=$$∫$$06$$  $$(2t2$$−$$t33)dt$$ ⇒θ−$$0=(2t33$$−$$t43$$×$$4)60$$ ⇒θ$$=36rad$$ ⇒$$n=362$$π<$$6$$

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A pulley of radius 2m is rotated about its axis by a force F=20t-5t2 newton [where t is measured in second) applied tangentially. If the moment of Inertia of the pulley about its axis of rotation is 10kg- m2.The number of rotations made by the pulley before its direction of motion reversed is

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