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Instantaneous Axis of Rotation

75.A circular...

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75.A circular disc is rotating about its own axis.Two particles P,Q of disc are at disc are at distances 4cm,6cm from axis of rotation.The ratio of centripetal acceleration of P,Q is

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Solution

$C e n t r i p e t a l a c c e l e r a t i o n = a = - ω^{2} r . L e t t h e c e n t r i p e t a l a c c e l e r a t i o n s o f t w o p a r t i c l e s P a n d Q o n a d i s c r o t a t i n g a b o u t i t s o w n a x i s a r e a_{1} a n d a_{2} . T h e n t h e r a t i o o f t h e i r a c c e l e r a t i o n s a r e, \frac{a_{1}}{a_{2}} = \frac{ω^{2} r_{1}}{ω^{2} r_{2}} = \frac{r_{1}}{r_{2}} o r \frac{a_{1}}{a_{2}} = \frac{r_{1}}{r_{2}} = \frac{4}{6} = \frac{2}{3} .$

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