Classical Mechanics (Kibble & Berkshire) · Problem 10.6

The angular momentum principle — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · linear-momentum-centre-of-mass

Problem

A uniform ball of mass

M

and radius

a

can roll without slipping on the rough outer surface of a fixed sphere of radius

b

and centre

O

. Initially the ball is at rest at the highest point of the sphere when it is slightly disturbed. Find the speed of the centre

G

of the ball in terms of the variable

\theta

, the angle between the line

OG

and the upward vertical. [Assume planar motion.] Show that the ball will leave the sphere when

\cos\theta = \frac{10}{17}