Rolling Ball

A spherical ball of mass M and radius R s l i p s slips on a horizontal plane. At some instant, it has translational velocity v 0 v_{0} and rotational velocity about the centre O, v 0 2 R \frac {v_{0}}{2R} . Then, the rotational velocity of the ball after it starts rolling perfectly is given by-

8 9 \frac {8}{9} v 0 v_{0} 6 7 \frac {6}{7} v 0 v_{0} 5 6 \frac {5}{6} v 0 v_{0} 2 3 \frac {2}{3} v 0 v_{0}

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3 solutions

Rishav Koirala
Mar 26, 2014

*The ball is slipping, so take frictional force and frictional torque into account. *Make two equations, one for translational or linear motion of the ball and the other for the rolling motion. *After the ball starts pure rolling, V = Rω and A = Rα. *Cancel 'time' from your equations. *Finally, write final linear velocity and final angular velocity in terms of v 0 v_{0}

Basic angular momentum conservation. Conserve it about the lowest point so that you don't have to worry about the torque due to friction. The equation is Angular momentum L = Ic \omega + r x MV

Amrit Agrahari - 7 years, 2 months ago

friend Can you please tell me the solution in details\

ashutosh mahapatra - 7 years, 2 months ago

THANK U...can u give me the 2 equations....i cannot figure them out...

Poorva Patel - 7 years, 2 months ago
Amrit Agrahari
Mar 31, 2014

Basic angular momentum conservation. Conserve it about the lowest point so that you don't have to worry about the torque due to friction. The equation is Angular momentum L = Ic \omega + r x MV

Yash Ghaghada
Sep 21, 2017

Conserve angular momentum

Taking v0 equal to u......

mur + iu/2r = mvr + iv/r

i=moment of inertia

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