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  4. A wheel having radius 10 cm is coupled by a belt to another wheel of radius 30cm. 1st wheel increases its angular speed from rest at a uniform rate of 1.57 rad s-2 The time for 2nd wheel to reach a rotational speed of 100 rev/min is...(assume that the belt does not slip)

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Q. A wheel having radius 10 cm is coupled by a belt to another wheel of radius 30cm. 1st wheel increases its angular speed from rest at a uniform rate of 1.57 rad $s^{-2}$ The time for 2nd wheel to reach a rotational speed of 100 rev/min is...(assume that the belt does not slip)

Solution:

At any instant linear acceleration of all points of coupled belt is same.
$a = r \, \alpha$
$r_1 \alpha_1 = r_2 \alpha_2$ find $\alpha_2$
$\omega_2 = \omega_1 + \alpha_2 t$
$t = \frac{\omega_2}{\alpha_2} $ $\because \, \omega_1 = 0$