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

Step-by-step solution

Initial moment of inertia of the wheel, I₁ = 0.500 kg-m ^2 Initial angular speed, ₁ = 20.0 rad/s Mass of the particle, m = 200 g = 0.200 kg Radius of the wheel, r = 20.0 cm = 0.200 m Moment of inertia of the particle about the axis of rotation, I_p = m r^2 = 0.200 (0.200)^2 = 0.008 kg-m ^2 Final moment of inertia of the system, I₂ = I₁ + I_p = 0.500 + 0.008 = 0.508 kg-m ^2 By the principle of conservation of angular momentum: I₁ ₁ = I₂ ₂ 0.500 20.0 = 0.508 ₂ ₂ = 10.0 0.508 19.7 rad/s