Question 464: Centre of Mass and Rotational Motion

Question

Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around is periphery as shown in the figure.Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad s$$-$$1.The value of n, to the nearest integer, is __________.[Given : In one complete revolution, the disk rotates by 6.28 rad]

Accepted Answer

$$\alpha  = {	au  \over I} = {{F.R.} \over {m{R^2}/2}} = {{2F} \over {mR}}$$
$$\alpha  = {{2 	imes 200} \over {20 	imes (0.2)}} = 10$$ rad/s
2
$${\omega ^2} = {\omega _0}^2 + 2\alpha \Delta 	heta $$
$${(50)^2} = {0^2} + 2(10)\Delta 	heta $$
$$ \Rightarrow \Delta 	heta  = {{2500} \over {20}}$$
$$\Delta 	heta  = 125$$ rad
No. of revolution $$ = {{125} \over {2\pi }} \approx 20$$ revolution

Centre of Mass and Rotational Motion

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