Introduction to Classical Mechanics · Problem 12.8

Relativity (Dynamics) — Morin

Physics — Mechanics · relativistic-force-momentum

Problem

Consider a dumbbell made of two equal masses,

m

. The dumbbell spins around, with its center pivoted at the end of a stick. If the speed of the masses is

v

, then the energy of the system is

2\gamma m

. Treated as a whole, the system is at rest. Therefore, the mass of the system must be

2\gamma m

. (Imagine enclosing it in a box, so that you can't see what's going on inside.) Convince yourself that the system does indeed behave like a mass of

M = 2\gamma m

, by pushing on the stick (when the dumbbell is in the ``transverse'' position shown in the figure) and showing that

F \equiv dp/dt = Ma