Answer to Question #258217 in Physics for Nick

Question

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.

Answer 1

(i) See below:

(ii) Apply rotational and translational laws:

$$-ma=T-mg,\\ I\alpha=Tr→I\frac ar=Tr,\\\space\\ T=m(g-a),\\\space\\ I\frac ar=mgr-mar,\\\space\\ a=0.285\text{ m/s}^2,\\ \alpha=1.43\text{ rad/s}^2,\\ \omega=\alpha t=6\text{ rad/s},\\ n=\omega/(2\pi)=0.95\text{ s}^{-1}.$$