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Shear Strain

A sphere is r...

Question

A sphere is rolling on a rough surface without any slipping at the point of contact. Find the radius of curvature of the trajectory of the point A when it is at a distance R/2 above the centre of the sphere.

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Solution

$T h e t r a j e c t o r y o f t h e p o i n t A a t d i s \tan c e \frac{R}{2}, w h e r e R i s t h e r a d i u s o f t h e s p h e r e i s a \sin u s o i d a l h a r m o n i c w a v e o f a m p l i t u d e \frac{3 R}{2}, o n t h e r o u g h s u r f a c e .$

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