Motion of Rigid Body
The
conditions necessary for the equilibrium of a rigid body are :
1.
Translational
equilibrium
The
resultant force on the rigid body is zero,
and
2.
Rotational
equilibrium
The
resultant torque ( or turning moment) on the rigid body
about
any axis is zero.
The
torque ( or turning moment ) :
Centre of
mass
Demonstration of
Centre of mass
If
a single force does not act through the centre of mass of a body, the
motion of a body will involve rotation. The
rotation takes place about the centre of mass.
moment
of inertia : 
The value of I
depends on :
(1)
the mass of the body,
(2)
the way the mass is
distributed, and
(3)
the axis of rotation.
Theorem about the
Moment of Inertia
1.
Parallel
Axes Theorem
I
= Ic.m. + M h2
2.
Perpendicular
Axes Theorem
Iz
= Ix + Iy
The
angular momentum
of a particle
about an axis is the product its linear momentum and the perpendicular
distance of the particle from the axis.
The
Rotational Form of Newton’s Second Law
The
Principle of Conservation of Angular Momentum
The total angular
momentum of a system remains constant provided no net external torque
acts on the system. Examples of conservation of angular momentum :
Ice-skater, High-diver
The
Combined Translational and Rotational Motion of a Rigid Body
The total kinetic energy of the body
=
Rotational K.E. + Translational K.E.
Motion
of a car round a circular track
