Question

A man of mass m=80kg runs at speed u=4m/s along the tangent to a disk-shaped platform of mass M=160kg and radius R=2m. The platform is initially at rest but can rotate freely about the axis through its center. Find the new angular velocity after the man step on the platform. (treat the man as particle).

Answer 1

Mass of the platform = M = 160 kg

Radius of the platform = R = 2 m

Moment of inertia of the platform = I

I = MR²/2

I = (160)(2)²/2

I = 320 kg.m²

Mass of the man = m = 80 kg

Initial speed of the man = u = 4 m/s

Initial angular velocity of the platform = ₁ = 0 rad/s (At rest)

Angular velocity of the platform after the man steps on the platform = ₂

By conservation of angular momentum,

I₁ + muR = (I + mR²)₂

(320)(0) + (80)(4)(2) = [320 + (80)(2)²]₂

₂ = 1 rad/s

New angular velocity of the platform after the man steps on the platform = 1 rad/s