derivation of magnitude of centripetal force
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Centripetal force
Centripetal force
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si143:
i have the same book that you have
so i can see from that
but i want the complete derivation
thanks for your help
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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.
Now for the magnitude. Consider the distance traveled by the body over a small time increment
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.
Now for the magnitude. Consider the distance traveled by the body over a small time increment
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