Question

An odd-shaped object rotates at a speed of 10.0 rev/s. A small 25 g mass with moment of inertia I=1.5x10-6 kg·m2 is dropped onto the object at a distance of 4.5 cm from its center of mass. The odd-shaped object slows to a speed of 9.0 rev/s. What is the moment of inertia of the odd-shaped object?

Answer 1

Moment of inertia of the odd shaped object = I₁

Initial rotational speed of the odd-shaped object = ₁ = 10 rev/s

Mass of the small object = m = 25 g = 0.025 kg

Moment of inertia of the small object = I = 1.5 x 10^-6 kg.m²

Distance of the small object from the center of mass of the odd shaped object = d = 4.5 cm = 0.045 m

Moment of inertia of the small object about the center of mass of the odd shaped object = I₂

I₂ = I + md²

I₂ = 1.5x10^-6 + (0.025)(0.045)²

I₂ = 52.125 x 10^-6 kg.m²

Rotational speed of the system after the small object is dropped on the odd shaped object = ₂ = 9 rev/s

By conservation of angular momentum,

I₁ = 4.69 x 10^-4 kg.m²

Moment of inertia of the odd shaped object = 4.69 x 10^-4 kg.m²