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Wednesday, 1 March 2017

Motion of system of particles and rigid body I


CONCEPTS.

Centre of mass of a body is a point where the entire mass of the body can be supposed to be concentrated. For a system of n-particles, the centre of mass is given by
Torque τ :
The turning effect of a force with respect to some axis, is called moment of force or torque due to the force. Torque is measured as the product of the magnitude of the force and the perpendicular distance of the line of action of the force from the axis of rotation.
Angular momentum
                                                          
It is the rotational analogue of linear momentum and is measured as the product of linear momentum and the perpendicular distance of its
line of axis of rotation.

Mathematically:  Ifis linear momentum of the particle and ⃗ its position vector, then angular momentum of the particle,
(a)In Cartesian coordinates :
(b)In polar coordinates : 

Where φ is angle between the linear momentum vector
and the position of vector

S.I unit of angular momentum is kg m2s-1

Geometrically, angular momentum of a particle is equal to twice the product of mass of the particle and areal velocity of its radius vector about the given axis.

Relation between torque and angular momentum:
(i)
(ii) If the system consists of n-particles, then
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