The kinetic energy of the two rings are equal and the ratio of their angular velocity is 4:3. Find the ratio of their moment of inertia.

CONCEPT:

Moment of inertia

• It plays the same role in rotational motion as mass plays in linear motion. It is the property of a body due to which it opposes any change in its state of rest or of uniform rotation.
• The moment of inertia of a particle is given as,

where r = perpendicular distance of the particle from the rotational axis
Rotational kinetic energy

• The energy, which a body has by virtue of its rotational motion, is called rotational kinetic energy.
• A body rotating about a fixed axis possesses kinetic energy because its constituent particles are in motion, even though the body as a whole remains in place.
• Mathematically rotational kinetic energy can be written as,

Where I = moment of inertia and ω = angular velocity

CALCULATION:

Given  and KE₁ = KE₂ = KE

• Rotational kinetic energy is given as,

     -----(1)

     -----(2)

Since KE₁ = KE₂,

• Hence, option 2 is correct.