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Angular momentum of rigid body
Intermediate
About a fixed axis, L equals Iω.
L = IωAbout a fixed axis L = Iω along the axis. For general rotation L = I·ω with a tensor I and need not be parallel to ω.
A 0.1 kg·m² wheel at 40 rad/s: 4 kg·m²/s.
L and ω can point in different directions for asymmetric bodies.
In more detail
For a rigid body rotating about a fixed axis, the angular momentum is L = Iω. The moment of inertia determines how the angular velocity relates to the angular momentum.
Real-world uses
- Flywheels and turbines carry large amounts of angular momentum.
- Spinning tops and gyroscopes are described by their angular momentum.
- A spinning wheel on a fixed axle has angular momentum equal to its moment of inertia times its angular velocity.
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Frequently asked questions
Is L always parallel to ω?
Only for rotation about a principal axis, which is a special case.
What units are used?
Kilogram metres squared per second.
When is L equal to Iω?
For a rigid body rotating about a fixed axis of symmetry, where the angular velocity is parallel to that axis.
Related topics in Rotational Motion
Race of rolling bodies · Work and power in rotation · Angular momentum of a particle · Torque and angular momentum · Conservation of angular momentum · Spinning skater and diver