### Angular Momentum

The angular momentum of a mass rotating in a circle of radius with angular velocity (rad/s), is defined by

where denotes the mass moment of inertia of the rigid body (§B.4.4).

#### Relation of Angular to Linear Momentum

Recall (§B.3) that the momentum of a mass traveling with velocity in a straight line is given by

while the angular momentum of a point-mass rotating along a circle of radius at rad/s is given by

where . The tangential speed of the mass along the circle of radius is given by

Expressing the angular momentum in terms of gives

 (B.18)

Thus, the angular momentum is times the linear momentum .

Linear momentum can be viewed as a renormalized special case of angular momentum in which the radius of rotation goes to infinity.

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