(a) What is the magnitude of the angular momentum of the system relative to the center of mass? (b) What is the angular speed about the center of mass?

Question

A puck of mass m₁ = 65.0 g and radius r₁ = 4.20 cm glides across an air table at a speed of = 1.50 m/s as shown in Figure a. It makes a glancing collision with a second puck of radius r₂ = 6.00 cm and mass m₂ = 140 g (initially at rest) such that their rims just touch. Because their rims are coated with instant-acting glue, the pucks stick together and rotate after the collision

(a) What is the magnitude of the angular momentum of the system relative to the center of mass? (b) What is the angular speed about the center of mass?

Answer 1

Consevation of linear momentum: m₁v₁ = (m₁ + m₂) v₁₂

Conservation of angular momentum: r_COM,1m₁v₁ = I_totω

r_COM,1 = (m₂/(m₁ + m₂))(r₁ + r₂)

I_tot = I₁ + I₂ + I_{parallel axis}

I₁ = (1/2)m₁r₁²

I₂ = (1/2)m₂r₂²

I_{parallel axis} = m₁r_COM,1² + m₂r_COM,2² = ((r₁+r₂)m₂/(m₁+m₂))²m₁ + ((r₁+r₂)m₁/(m₁+m₂))²m₂

That should do it. Good luck!