# Motion of system of particles and rigid body III

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Moment of inertia and angular momentum: The moment of inertia of a rigid body about an axis is numerically equal to the angular momentum of the rigid body, when rotating with unit angular velocity about that axis.
Mathematically: K.E of rotation = 1/2 lω2

Moment of inertia and kinetic energy of rotation: The moment of inertia of a rigid body about an axis of rotation is numerically equal to twice the kinetic energy of rotation of the body, when rotation with unit angular velocity about that axis.
Mathematically: K.E of rotation = 1/2 Iω2

Moment of inertia and torque: The moment of inertia of a rigid body about an axis of rotation is numerically equal to the external torque required to produce a unit angular acceleration in the body BOUT THE GIVEN AXIS.
Mathematically: τ = Ia

Law of conservation of angular momentum: If no external torque acts on a system, the total angular momentum of the system remains unchanged.
Mathematically:
Iω = constant vector, i.e.,in magnitude, I1ω1 = I2ω2

Provides no external torque acts on the system

For translational equilibrium of a rigid body,

For rotational equilibrium of a rigid body,

• The following table gives a summary of the analogy between various quantities describing linear motion and rotational motion
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