A rolling sphere

Classical Mechanics Level 2

Assuming no slipping, a spherical ball of radius 10 cm 10\text{ cm} is rolling at an angular velocity 2 rad/s 2 \text{ rad/s} (on an axis parallel to the floor) find the speed ( in m/s \text{m/s} ) of the ball at its center.


The answer is 0.2.

Yoon Ho Seol by Yoon Ho Seol , 26, USA

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2 solutions

Rishabh Tiwari
May 16, 2016

Calculating the speed of the centre of the ball is same as calculating its linear velocity, since the centre moves in a straight line..hence by definition of linear velocity,

V= w × r = 0.1 × 2 = 0.2 m/s.

Thank you.

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Yoon Ho Seol
May 16, 2016

At the center of a rolling circle the velocity equals radius x angular velocity. Likewise on a sphere the center speed would be 0.1m x 2m/s = 0.2m/s.

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