# Experiments regarding C of A.M.

1. Apr 19, 2004

### ACLerok

I'm in desperate need of any testing experiment that shows the conservation of angular momentum. It should be something where an objects shape or radius changes while it spins, and calculate the angular momentum at each moment in time to see if it's conserved. If anybody has any ideas at all, PLEASE leme know! Thanks

2. Apr 19, 2004

### sridhar_n

...

Why don't u consider making ur own Gyroscope...and spin it while sitting in a chair such that its axis of spin is perpendicular to the ground. Now make it parallel to the ground . U will find that the chair now rotates

3. Apr 19, 2004

### arildno

Well, this is possibly a dumb thought experiment that can't be realized in practice, but anyways:
Attach to a vertical rod L a spring K standing normal to L.
K is sufficiently stiff so that it can't bend downwards much.
Attach to K at the end an object O of mass m.
Apply an external torque T to L, such that the system rotates around the axis L with angular velocity w0.
Due to the centrifugal force on O, K will stretch a bit in its length direction.
Now remove T, and assume that L is free to rotate about the vertical but that it's centerline doesn't move (for example, placing the lower part of L in a closely fitting container.
We assume that the friction between the container wall and L is negligible, at least over the duration period of the experiment.

MECHANISM OF CONSERVATION OF ANG. MOM::
Since we neglect the effect of friction on L from the container, changes in angular velocity w(t), should come from the dynamics associated with O.

The only forces acting on O is the centrifugal force, the spring force, and gravity.
I will assume that the motion of O remains 2-dimensionsial, in the plane normal to L.
(This is probably incorrect; I suspect rod L would jump up and down somewhat, being correlated with the interplay of gravity and the spring force's component normal to K's length direction, making O oscillate somewhat in the vertical.)

We look at the component of angular momentum along L.
In the 2-D approximation, we see:
a) The forces on O (centrifugal and spring force) are radial (along K), and, so the rate of change of angular momentum along L should be zero.
b) The 2-D approximation implies therefore that m*r(t)^(2)w'(t)=constant.
(r(t) is K's length at t)
The prediction should therefore be:
When K contracts, w(t) should increase, when K lengthens, w(t) should decrease..