Introduction to Classical Mechanics · Problem 6.39

The Lagrangian method — Morin

Physics — Mechanics · conservation-laws

Problem

Bead on stick, using

F = ma

* After doing Problem 6.8, show again that the quantity

E

is conserved, but now use

F = ma

. Do this in two ways: (a) Use the first of Eqs. (3.51). Hint: multiply through by

\dot{r}

. (b) Use the second of Eqs. (3.51) to calculate the work done on the bead, and use the work--energy theorem.