System of Particles and Rotational Motion Centre of Mass and Rotational Motion

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SYSTEM OF PARTICLES AND ROTATIONAL MOTION
CENTRE OF MASS AND ROTATIONAL MOTION
INTRODUCTION-
For describing the motion of rigid bodies, we shall introduce the key concept of ‘centre of mass’. This concept enables us to understand how we can apply justifiably the Newton’s laws of motion, in essentially the same form to objects of large size including even the astronomical objects like the planets and the stars.
KINDS OF MOTION OF A RIGID BODY-
A rigid body may have three kinds of motion-
(1) Pure Translation Motion- in such a motion, every particle of the body has the same velocity at a particular instant of time. For e.g. when a rectangular block slides down an inclined plane, any point like P1,P2 of the block, at any instant of time
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Hence the centre of mass is closer to the massive particle. NOTE- 1. The centre of mass may lie outside the object. For e.g. the centre of mass of ring lies outside it. 2. Centre of mass depends on the distribution of mass within the body and is closer to heavy part but for identical particles C.M. lies at the midpoint of the line joining the point masses. 3. If an object is symmetrical and have uniform distribution of mass then its C.M. coincides with geometrical centre. 4. The position of C.M. is independent from the coordinate system. E.g. the centre of mass of a ring of uniform thickness is at its centre whatever be the coordinate system. CENTRE OF MASS OF LAMINAR OBJECTS-
A laminar object means a two dimensional distribution of mass of negligible thickness e.g. paper of your copy. If a large number of laminar type objects are placed in a plane then

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