2
$\begingroup$

I understand angular velocity increasing since the distance becomes shorter but why does the actual angular velocity increase? There is no force being applied perpendicular to the centripetal force so why does the velocity increase?

$\endgroup$
2
$\begingroup$

When the radius is decreased, there exists a component of velocity which is radially inward. The dot product of this component with the centripetal force is not zero, so work is done and speed increases.

Another way to think of it is that as an orbiting object falls deeper into a gravity well, it loses potential energy and gains kinetic energy, which means that speed increases.

$\endgroup$
0
$\begingroup$

Angular momentum is given by the cross-product of the momentum and the position vector. If one assumes these two vectors are orthogonal then the magnitude of the angular momentum is the product of the magnitudes of these two vectors. Hence if the angular momentum remains constant and the magnitude of one of these vectors decrease then the other one must increase. Since angular momentum in a closed system is conserved, a decrease in the distance would induce an increase in the momentum.

$\endgroup$
  • $\begingroup$ But why is it an increase velocity instead of mass? Obviously the mass doesn't increase (in Newtonian mechanics anyway) however your explanation doesn't address this. Intuitively why is it that the velocity specifically increases? $\endgroup$ – Ray Kay Aug 12 '16 at 11:22
  • $\begingroup$ Not sure if one can give a general mechanism for this that would be applicable to all cases. In the answer of EL_DON there are explanations of some cases. Perhaps one can say that if you have something that you are swinging on a rope and you want to shorten the length of rope, you would need to pull it in. This pull would produce a force giving an inward acceleration, which would then increase the angular velocity. $\endgroup$ – flippiefanus Aug 12 '16 at 12:55

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.