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## Homework Statement

For each of the following potential energy functions in three dimensions, what quantities are conserved (energy, momentum, angular momentum)?

## Homework Equations

U = k/2(x^2 + y^2)

U = α/r

U = β(z(hat) dotted with

**r**)^2

U = α/r + β(z(hat) dotted with

**r**)^2

Where z(hat) is the unit vector in the z direction.

## The Attempt at a Solution

So I understand that in order for the angular momentum to be conserved the cross product of

**r**and

**F**, being the force obtained from the negative gradient of U, must be equal to zero. However I am not sure what to use for the position vector

**r**.

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