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The **angular momentum**, *L* of a rigid body with
moment of
inertia *I* rotating with angular velocity is:

L = I.
| (14) |

The dynamical torque equation can be written in terms of angular
momemtum:

= |
I
| ||

= |
I
| ||

= | |||

= | . | (15) |

**Idea: ****Conservation of Angular Momentum**

In the absence of external torque
( = 0) , the
angular momentum
of a rotating rigid body is conserved
*L* = 0 ,
or

I_{i} = I_{f}.
| (16) |

For systems that consist of many rigid bodies and/or
particles, the total angular momentum about any axis is the
sum of the individual angular momenta. The **conservation of angular moment** also applies to such
systems. In the
absence of external forces acting on the system, the total
angular momentum of the system remains constant.

**Note: **

- Angular momentum and torque are really
*vector quantities*. For two dimensional motion they always point either out of the page (if they are positive) or into the page (if they are negative). Thus we don't need to explicitly consider their vector properties. We need only insure that we have the correct sign. - Table 8.1 gives the rotational analogues of some
linear
quantities.

**Table 8.1:**Linear vs. Angular QuantitiesLinear Stuff Angular Stuff Quantity Units Quantity Units *a**m*/*s*^{2}*rads*/*s*^{2}*m**kg**I**kg**m*^{2}*p*=*mv**kg**m*/*s**L*=*I**kg**m*^{2}/*s**KE*_{t}=*mv*^{ 2}*J**KE*_{r}=*I**J**F*=*ma**N*= *I**N**m*

10/9/1997