Question

a rotating boby with moments of inertia 6×10^-4 kg m^2 has a kinetic energy 12j the angular momentum of a body is​

Answer 1

Given :

Moment of inertia = 6 × 10‾⁴ kg m²

Kinetic energy = 12 J

To Find :

Angular momentum of the body.

Solution :

❖ The moment of inertia of a rigid body depends on the mass of the body, its shape and size, distribution of mass about the axis of rotation and the position and orientation of the axis of rotation.

• First of all we have to find angular velocity of the body.

➙ K = 1/2 I ω²

» K denotes kinetic energy

» I denotes moment of inertia

» ω denotes angular velocity

By substituting the given values;

➙ 12 = 1/2 × (6 × 10‾⁴) × ω²

➙ 4 × 10⁴ = ω²

➙ ω = 2 × 10² rad/s

♦ Angular momentum of the body :

It is measured as the product of moment of inertia and angular velocity$.$

➠ L = I ω

➠ L = 6 × 10‾⁴ × 2 × 10²

➠ L = 12 × 10‾²

➠ L = 0.12 kg m²/s