The centripetal force acting on a particle moving in a circular in a path depends on mass (m), velocity (v), and radius (r), of circular path. Derive its formula.

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Solution

$W h e n e v e r a b o d y o r a p a r t i c l e d o e s c i r c u l a r m o t i o n t h e n a f o r c e w o r k s o n t h e m w h i c h i s a l w a y s d i r e c t e d t o w a r d s t h e c e n t e r o f t h e c i r c u l a r p a t h, w h i c h i s c a l l e d C e n t r i p i t a l F o r c e . T h e F o r c e r e q u i r e d t o g i v e c i r c u l a r m o t i o n t o p a r t i c l e o r t o t h e b o d y . T h e m a g n i t u d e o f a c c e l e r a t i o n i s v^{2} / r . A c c o r d i n g t o N e w t o n' s l a w, t h e p a r t i c l e m u s t b e u n d e r t h e a c t i o n o f e x t e r n a l f o r c e i n o r d e r t o h a v e t h i s a c c e l e r a t i o n . F = m a = m \frac{v^{2}}{r} I n t e r m s o f A n g u l a r v e l o c i t y, ω F = m ω^{2} r$

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A particle of mass m is revolving in a circular path of radius r. Its angular momentum is L. The centripetal force acting on the particle is

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