Classical Dynamics of Particles and Systems · Problem 11-9

Coupled Oscillations — Marion & Thornton

Physics — Mechanics · slab-on-cylinder-stability

Problem

A homogeneous slab of thickness

a

is placed atop a fixed cylinder of radius

R

whose axis is horizontal. Show that the condition for stable equilibrium of the slab, assuming no slipping, is

R > a/2

. What is the frequency of small oscillations? Sketch the potential energy

U

as a function of the angular displacement

\theta

. Show that there is a minimum at

\theta = 0

for

R > a/2

but not for

R < a/2