Question

A constant external torque τ acts for a very brief period Δt on a rotating system having moment of inertia I.

(a) The angular momentum of the system will change by τ Δt.

(b) The angular velocity of the system will change by τ Δt/ i.

(c) If the system was initially at rest, it will acquire rotational kinetic energy (τ Δt)² / 2I.

(d) The kinetic energy of the system will change by (τ Δt)²/ I.

Answer 1

Correct Answer is: (a, b, & c)

Let L = angular momentum.

τ = dL/dt or dL = τ dt.

For constant torque,

ΔL = τ Δt = I Δω  or Iω if ω_i = 0.

Rotational kinetic energy = 1/2 Iω² = (ΔL)²/2I