Question

A wheel of moment of inertia $0.500$ kg-$m^2$ and radius $20.0$ cm is rotating about its axis at an angular speed of $20.0$ rad/s. It picks up a stationary particle of mass $200$g at its edge. Find the new angular speed of the wheel.

Answer 1

A wheel has moment of inertia $I=0.500kg-m^2$

The radius of wheel is $r=0.2m$

The angular velocity of the wheel is $\omega =20rad/s$

Mass of the Stationary paticle $=0.2kg$

Therefore

$I_1{\omega }_1=I_2{\omega }_2$ (since external torque $=0$)

$I_1{\omega }_1=(I_1+M{R}^2){\omega }_2$

$\Rightarrow 0.5\times 10=0.5+0.2\times {0.2}^2){\omega }_2$

$\Rightarrow 10/0.508={\omega }_2=19.69=19.7rad/s$