Question 454: Centre of Mass and Rotational Motion

Question

A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s is ____________ $$\pi$$ $$	imes$$ 10$$-$$1 Nm.

Accepted Answer

$$	au  = {{\Delta L} \over {\Delta t}} = {{I({\omega _f} - {\omega _i})} \over {\Delta t}}$$
$$	au  = {{{{m{R^2}} \over 2} 	imes [0 - \omega ]} \over {\Delta t}}$$
$$ = {{10 	imes {{(20 	imes {{10}^{ - 2}})}^2}} \over 2} 	imes {{600 	imes \pi } \over {30 	imes 10}}$$
$$ = 0.4\pi  = 4\pi  	imes {10^{ - 2}}$$

Centre of Mass and Rotational Motion

A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s is ____________ $\pi \times 10-$1 Nm.

Choose the correct answer: