0
$\begingroup$

I have a doubt, I hope you can help me. In the case of a spinning top precessing around the $y$-axis, there's a torque $\vec \tau$ which comes from the weight of the toy. This torque is perpendicular to the angular momentum $\vec L$. We have the relation: $$ \frac{d\vec L}{dt} = \vec \tau$$ I understand angular momentum changes its direction, but why not the module?

$\endgroup$
0
$\begingroup$

This is formally equivalent to the fact, that a magnetic field does not change the magnitude of a velocity. The answer is, because the torque is perpendicular to the angular momentum (as you point out, cast in math $\vec L \cdot \vec \tau = 0$). Then it is a one liner: $$\partial_t \left|\vec L\right| = \frac{2 \vec L \cdot \dot{\vec L}}{2 \sqrt{\vec L \cdot \vec L}} = \frac 1 {\left|\vec L\right|}\vec L \cdot \vec \tau = 0.$$

$\endgroup$
  • $\begingroup$ Just one question: the formula you wrote, i haven't reached that level of math. Is it partial derivative of angular momentum? If so, what should i read to understad the rest of the equation. Thank you $\endgroup$ – Omar Jul 14 '15 at 0:29
  • $\begingroup$ You can also understand it geometrically. And yes, it is a partial derivative of the modulus of the angular momentum with respect to time. I guess any maths in physics book will do. $\endgroup$ – Sebastian Riese Jul 15 '15 at 19:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.