A rope is wound around a hollow cylinder of mass $$3$$ kg and radius $$40$$ cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of $$30$$ N ?

Question

Infinity Learn · Accepted Answer

$$m=3$$ kg,$$r=40$$ $$cm=40$$×$$10-2$$ m,$$F=30$$ NMoment of inertia of hollow cylinder about its axis $$=mr2=3$$ kg×$$(0.4)2$$ $$m2=0.48$$ kg $$m2The$$ torque is given by, τ$$=I$$αwhere I $$=$$  moment of inertia, α$$=$$ angular acceleration  In the given case, τ$$=rF$$, as the force is acting  perpendicularly to the radial vector. ∴  α$$=$$τ$$I=Frmr2=Fmr=303$$×$$40$$×$$10-2=30$$×$$1003$$×$$40$$ α$$=25rads-2$$

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ?

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