Answer to Question #258217 in Physics for Nick

Question #258217

FIGURE 2 shows a 1.5 kg block is hung by a light string which is wound around a

smooth pulley of radius 20 cm. The moment of inertia of the pulley is 2 kg m2


(i) Sketch the free body diagram of the 1.5 kg block.

(ii) When the mass is released from rest, calculate the angular velocity and number of

revolutions of the pulley at t = 4.2 s.


1
Expert's answer
2021-10-31T18:12:28-0400

(i) See below:



(ii) Apply rotational and translational laws:


ma=Tmg,Iα=TrIar=Tr, T=m(ga), Iar=mgrmar, a=0.285 m/s2,α=1.43 rad/s2,ω=αt=6 rad/s,n=ω/(2π)=0.95 s1.-ma=T-mg,\\ I\alpha=Tr→I\frac ar=Tr,\\\space\\ T=m(g-a),\\\space\\ I\frac ar=mgr-mar,\\\space\\ a=0.285\text{ m/s}^2,\\ \alpha=1.43\text{ rad/s}^2,\\ \omega=\alpha t=6\text{ rad/s},\\ n=\omega/(2\pi)=0.95\text{ s}^{-1}.


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