Question

Show that any equation of motion is dimensionally correct.

Answer 1

Answer:

So velocity has dimensions of , momentum has dimensions of , and the time derivative of momentum has dimensions of , the same as force. Then there's the Lagrangian equation of motion: ... The RHS of the first equation has units of energy per length, or , so the first equation is dimensionally correct.

Answer 2

Answer:

So velocity has dimensions of , momentum has dimensions of , and the time derivative of momentum has dimensions of , the same as force. Then there's the Lagrangian equation of motion: ... The RHS of the first equation has units of energy per length, or , so the first equation is dimensionally correct.