1. 1 5. Conservation of angular momentum One particle Angular momentum:Torque: Newton’s second Law for rotation: Conservation of angular momentum: Compare with:

2. 2 a)An infinite homogenous xy-plane. P x, P y, M z (the plane is xy-plane) b)An infinite homogenous cylinder. P z, M z (the axis of the cylinder is the z- axis c)An infinite homogenous prism. P z, (the edges of the prism are parallel to the z- axis) d)Two points. M z (the line joining points is the z- axis) e)An infinite homogenous half-plane. P y (the edge of the plane is y-axis) f)A homogenous cone. M z (the axis of the cone is the z- axis) g)An homogenous circular torus. M z (the axis of the torus is the z- axis) Example: Which components of momentum and angular momentum are conserved in motion in the fields of the following objects?

3. 3 System of particles

4. 4 Some properties of angular momentum y'y 1)Moment of inertia depends on the choice of origin except when the system is at rest (i.e. P = 0). This indeterminacy does not affect the low of conservation of angular momentum, since the linear momentum is also conserved in a closed system. x' x y x 2) If R is the position of the center of mass of the system of particles, then the angular momentum is a sum of “intrinsic” angular momentum L cm about the center of mass and the angular momentum of the center mass.

5. 5 Some properties of angular momentum (continued) 3) The derived equations and therefore the conservation of angular momentum hold true even if the CM is being accelerated and so is not fixed in an inertial frame.