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Centripetal Acceleration

A particle of...

Question

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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Solution

Angular momentum is given by
m x v x r=L (given)
so velocity of the particle is , $V equals fraction numerator L over denominator m cross times r end fraction$
centripetal force is given by $fraction numerator m V squared over denominator r end fraction$
so centripetal force is $fraction numerator m open parentheses begin display style fraction numerator L over denominator m r end fraction end style close parentheses squared over denominator r end fraction equals fraction numerator m L squared over denominator m squared r cubed end fraction equals fraction numerator L squared over denominator m r cubed end fraction$

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