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a small sphere of radius r starts rolling from rest on a fixed sphere of radius R.find the angular velocity of the small sphere at that instant when it leaves contact with the sphere of radius R.

a small sphere of radius r starts rolling from rest on a fixed sphere of radius R.find the angular velocity of the small sphere at that instant when it leaves contact with the sphere of radius R.

Grade:11

1 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

assuming pure rolling, there is no loss of energy due to friction

while rolling, v=rω,

using elementary trigonometry, one can calculate loss of potential energy, i.e., kinetic energy as a function of angle between vertical and the radius vector of small sphere(point P) from centre of fixed sphere (point O).

kinetic energy=(m/2)v2+(I/2)ω2

centripetal force= (component of gravitational force on small sphere directed along PO)minus(normal reaction)

centripetal force=v2/R

loss of contact occurs when normal reaction becomes zero.

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