Conervation of TOTAL Momentum

[justadream]

Can someone confirm if this is an example of total momentum being conserved (with some angular momentum being converted to linear momentum)?

This is based on TBR page 211 #45

If you are on a rotating platform and holding masses in your hand and then drop them, your angular velocity will remain constant.

This is because after dropping the masses, they will move (in a linear fashion - tangential to the circle).

Thus, it appears some of the original angular momentum is being converted to linear momentum.

The total momentum between the two systems (the person and the weights) is unchanged.

---

Members don't see this ad.

 

[Cawolf]

That is an interesting viewpoint, but not one I have heard - I always understood linear and angular momentum to be conserved separately.

One could say that the masses already have translational momentum that is being constrained circularly and upon their release move in a linear fashion that is tangent to the prior rotation.

Releasing the mass decreases the moment of inertia of the platform and accordingly the angular momentum.

I would be interested to hear more from a more experienced person though.

 

[justadream]

@Cawolf

"One could say that the masses already have translational momentum that is being constrained circularly"

Using this definition, is there any point to define angular momentum?

 

[Cawolf]

That's the question! 😉

I am not really sure - there is definitely is a point as far as predicting behavior and performing calculations - but for the objects that are released, you really are saying the same thing both ways.

As I prefaced in the first post, I don't really know the technical answer - but I have always heard of them being conserved independently (what value that has I am not sure). They don't have the same units even - so I am not sure how you would compare it if you set up that problem and calculated the initial and final momentum of the system.

 

[techfan]

Basically whats happening is that the angle between the vectors changes, so it seems like the cross product does too (and therefore the angular momentum) but the length of the radius vector is also changing cancelling out the effect of the changing angle

 

[milski]

There is no such thing as conversion between linear and angular momentum - the two are different quantities and are preserved independently of each other.

The picture from techfan should give you a good idea of what is going on. Something important to keep in mind - having a non-zero angular momentum is not the same thing as rotation. Even a body moving in a straight line can have a non-zero angular momentum, if that straight line does not go through the origin of the coordinate system. That follows directly from the definition of angular moment - L=r x p=r x mv (where L is the angular momentum, r - the position of the body, p its linear momentum, m its mass and v its linear velocity). For non-zero r and v, which are also not collinear, the cross product will be non-zero.