Question

A disc of mass 1kg and radius 0.1m is rotating with angular velocity 20 rad/s. what is angular velocity if a mass of 0.5kg is put on the circumference of the disc ?

Answer 1

mass of disc, m = 1kg
radius of disc , r = 0.1m
initial angular velocity of disc, $\omega_1$ = 20 rad/s

moment of inertia of disc about an axis normal to the plane of it and passing through its centre is given by , $I_1=\frac{1}{2}mr^2$
= 0.5 × 1 × (0.1)² = 0.005 kgm²

Moment of inertia of disc after putting a mass of 0.5kg on the circumference of disc. $I_2=I_1+m'r^2$
= 0.005 + (0.5) × (0.1)² = 0.005 + 0.005 = 0.01kgm²

now use conservation of angular momentum,
$\tau_{external}=0$ so, $I_1\omega_1=I_2\omega_2$

so, 0.005 × 20 = 0.01 × $\omega_2$

$\implies\omega_2=10rad/s$

Answer 2

Answer:

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