Angular momentum is a measure of the rotational motion of an object that depends on the object's rotational inertia and angular velocity. Angular velocity refers to the number of rotations per second. For an object rotating about an axis, its angular momentum can be calculated as the product of its mass, velocity, and the distance from the axis of rotation. Just as an external force is required to change an object's linear momentum, an external torque is needed to change an object's angular momentum. Angular momentum is conserved, as demonstrated when a figure skater pulls her arms in to spin faster or stretches out to spin slower, due to the relationship between rotational inertia and rotational velocity.

1. 4. Angular Momentum
▪ Angular momentum is:
= A measure of the rotational property of motion.
- - It depends upon the object's rotational inertia and
its angular (rotational ) velocity.
-- Angular velocity is the number of rotations per second.
▪ Angular momentum = rotational inertia x rotational velocity
* mass moving in a straight line has momentum.

2. 4. Angular Momentum
▪ Object is small compared to the radial distance to its axis of rotation,
the angular momentum can be simply expressed as the linear
momentum (mv) times its radius (r).
Angular momentum = mvr
▪ Just as an external force is required to change the linear momentum
of an object, an external net torque is required to change the angular
momentum of an object.
▪ Newton's first law of inertia for rotating objects in terms of angular
momentum.

3. 5. Rotational Physics
▪ Angular velocity (ω) is the time rate of angular displacement.
= Angular displacement (Ө) (measured in revolutions,
degrees or radians) per unit of time or the time rate of
angular displacement.
1 Revolution = 360o = 2π Radians = 1 Wavelength

4. 5. Rotational Physics
Angular displacement, theta (Ө), describes the angle or degrees an
object may be rotated about some fixed axis. This is comparable to
displacement in linear motion.
Angular velocity, Omega (ω) is measured in rev/s, o/s, or rad/s.
In linear of straight line motion we had we had velocity. Remember
that velocity is how fast an object goes in a particular direction. Now
we are concerned about how fast the object rotates or spin.
This direction of spin will be clockwise or counter clockwise.
Angular acceleration, alpha (ά) is the rate of change of angular
velocity. It is measured in rev/s2, o/s2, rad/s2 or some other
combination of appropriate units.

5. 6. Conservation of Angular Momentum
▪ Angular momentum is also conserved.
= A figure skate spinning, you will have noticed that when she
pulls her arms in tight she spins more quickly, and when she
stretches her arms out wide she spins more slowly.
- This demonstrates the conservation of angular momentum.
▪ Since angular momentum is a product of rotational inertia and
rotational velocity, changing one will change the other.
ex) When the mass is farther from the center, the rotational inertia
increases and the rotational velocity decreases.
- This also explains why divers in a tight tuck can spin more
quickly when diving.