Conservation of angular momentum

Deriving equation (13.3)Angular momentum obeys a separate conservation law from that of linear momentum. To best understand this conservation law we need to rewrite the equation for angular momentum. Recall that linear momentum is the product of mass and velocity, p = mv. We want a similar form of equation for the angular momentum in terms of the angular velocity ω. We start with equation (13.2) then use the fact that the linear velocity and angular velocity are related by v = ωr. Read the text aloud
If we regroup the terms, we find that the moment of inertia I in the angular momentum equation appears in the same place as the mass m in the linear motion equation. The result is equation (13.3), which tells us that angular momentum L is the product of moment of inertia I and angular velocity ω. Moment of inertia is the rotational analog of mass. Read the text aloud
(13.3) L=Iω
L  = angular momentum (kg m2/s)
I  = moment of inertia (kg m2)
ω  = angular velocity (rad/s)
Angular momentum
and moment of inertia
Recall that Newton’s first law says the linear momentum of an object remains constant when the net force is zero. A similar rule holds for angular momentum.

The angular momentum of a rotating body remains constant when there is
zero net torque acting on the body.
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Figure skaters and divers make use of angular momentum to perform feats of rotational agility. A skilled skater can increase her rate of spin to as much as five revolutions per second by pulling her arms close to her body. Platform divers tuck in their arms and legs while tumbling then open up their bodies to slow their rotation before hitting the water. Both techniques employ conservation of angular momentum. Read the text aloud
An ice skater sets up a fast spin by spinning slowly, with her arms and one leg extended. In the absence of any net torque, the skater’s total angular momentum is conserved. To spin faster, the skater reduces her moment of inertia I by pulling in her arms. To conserve L, her angular velocity ω increases! Read the text aloud Show What is her moment of inertia?
Angular momentum conservation and a spinning ice skater
When a platform diver wants to do a series of somersaults as part of his dive, why does he tuck his body into a tight ball? Show

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