Define centripetal acceleration and radial acceleration, obtain their expression.
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Define centripetal acceleration. Derive an expression for the centripetal a
Define centripetal acceleration. Derive an expression for the centripetal acceleration of a particle moving with uniform speed 'v' along a circular path of radius 'r'. Discuss the direction of the acceleration.
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Centripetal Acceleration. Centripetal acceleration is the rate of change of tangential velocity: Consider an object moving in a circle of radius r with constant angular velocity. The tangential speed is constant, but the direction of the tangential velocity vector changes as the object rotates.
A body that moves in a circular motion (of radius r) at constant speed (v) is always being accelerated. The acceleration is at right angles to the direction of motion (towards the center of the circle) and of magnitude v2 / r.
The direction of acceleration is deduced by symmetry arguments. If the acceleration pointed out of the plane of the circle, then the body would leave the plane of the circle; it doesn't, so it isn't. If the acceleration pointed in any direction other than perpendicular (left or right) then the body would speed up or slow down. It doesn't.