# Doubt in classical mechnaics

is it necessarily true that we have
$$\frac{\partial T}{\partial q}=0$$?

## Answers and Replies

I imagine kinetic energy often varies if a generalized coordinate of the system varies. I don't see why that derivative would be 0 in general.

For instance, if the generalized coordinate q describes the angular velocity of a body about some axis, and q varies while holding all other generalized coordinates constant, then the kinetic energy T of the system varies, and that derivative is non-0... right?

Andy Resnick
T=$\frac{1}{2}m (\dot{r}^{2} + (r\dot{\theta})^{2})$