System of Particles and Rotational Motion Centre of Mass and Rotational Motion
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 moves with the same velocity. This is because the block is a rigid body and all the particles of the body are moving together, with the same velocity.
(2) Pure Rotational Motion- in such a motion, a rigid body rotates about a fixed axis. Every particle of the body moves in a circle, which lies in a plane perpendicular to the axis, and has its centre on the axis. For e.g., in an oscillating table fan or pedestal fan, the axis of rotation is horizontal. This axis has an oscillating sideways movement in a horizontal plane about the vertical through the point at which the axis is pivoted.
(3) Combination Of Translational And Rotational Motion- for e.g., when a cylinder rolls down an inclined plane, its motion is a combination of rotation about a fixed axis and translation. As the cylinder shifts from top to the bottom of inclined plane, the points P1, P2, P3, P4 on the rolling cylinder have different velocities at a particular instant of time. If the cylinder were to roll without slipping, the velocity of the point of contact P3 would be 0, at any instant of time.
From the above discussion we conclude that-
(i) The motion of a rigid body, which is not provided or fixed in some way is either a pure translation or a combination of
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 moves with the same velocity. This is because the block is a rigid body and all the particles of the body are moving together, with the same velocity.
(2) Pure Rotational Motion- in such a motion, a rigid body rotates about a fixed axis. Every particle of the body moves in a circle, which lies in a plane perpendicular to the axis, and has its centre on the axis. For e.g., in an oscillating table fan or pedestal fan, the axis of rotation is horizontal. This axis has an oscillating sideways movement in a horizontal plane about the vertical through the point at which the axis is pivoted.
(3) Combination Of Translational And Rotational Motion- for e.g., when a cylinder rolls down an inclined plane, its motion is a combination of rotation about a fixed axis and translation. As the cylinder shifts from top to the bottom of inclined plane, the points P1, P2, P3, P4 on the rolling cylinder have different velocities at a particular instant of time. If the cylinder were to roll without slipping, the velocity of the point of contact P3 would be 0, at any instant of time.
From the above discussion we conclude that-
(i) The motion of a rigid body, which is not provided or fixed in some way is either a pure translation or a combination of