# Angular momentum in a half rotating body

1. May 5, 2013

### DiracPool

If we look at the classical formula for the conservation of angular momentum, L=mvr, we can easily see that, if the radius of a rotating body is shortened, its velocity must increase in order to conserve L, and vice-versa.

Again, the classical conception we have of this formula is its application to a spinning or rotating body, rotating in a unidirectional clockwise or counterclockwise fashion.

My question is this: Does this same formula hold for an object that is not going fully around a unit circle, say, but it oscillating back and forth through half of the circle. In other words, say it oscillates back and forth between 0 and Pi, confined to only the first and second quadrants of the circle. How would the dynamics of the system change in this circumstance? You would think that, even though you can assign a specific frequency to the back and forth oscillation, the fact that you would be constantly accelerating and decelerating in order to switch directions would constantly be shifting the radius of the oscillating object in order to conserve the angular momentum.

Is this assumption correct? Is there a different formula/equation that is used to model such an occurance?

Edit: Or is the deal here that conservation of angular momentum doesn't apply in this instance because energy/torque must continually be added to the system in order to keep switching directions?

Last edited: May 5, 2013
2. May 5, 2013

### Staff: Mentor

To oscillate back and forth, you need some non-radial force, and angular momentum cannot be conserved (unless something else oscillates in the opposite way, but then you have different velocities for different parts of the setup).

3. May 5, 2013

### DiracPool

Yeah, that makes sense. Thanks mfb.