Question

A wheel of moment of inertia 0⋅500 kg-m² 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

Given:
Initial moment of inertia of the system,
I₁ = 0.500 kg-m²;
r = 0.2 m;
ω = 20 rad/s
Mass of the stationary particle, m = 0.2 kg
Final moment of inertia of the system,
I₂ = I₁ + mr²
It is given:
External torque = 0
Angular momentum is conserved; therefore, we have:
$I_1{\omega }_1=I_2{\omega }_2$
$$\begin{gathered} \Rightarrow 0.5\times 20=\left(0.5+0.2\times {\left(0.2\right)}^2\right){\omega }_2 \\ \Rightarrow {\omega }_2=\frac{10}{0.508}\approx 19.7\mathrm{rad}/\mathrm{s} \end{gathered}$$