Angular momentum

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This gyroscope remains upright while spinning due to its angular momentum.
An ice skater conserves angular momentum—her rotational speed increases as her moment of inertia decreases by drawing in her arms and legs

In physics, the angular momentum of an object rotating about some point is the extent to which the object will continue rotating about that point unless acted upon by an external force (torque).

If a point mass rotates about an axis, then the angular momentum with respect to a point on the axis is related to

  1. the mass of the object,
  2. the velocity and
  3. the distance of the mass to the axis.

Angular momentum is a conserved quantity: a system's angular momentum stays constant unless an external torque acts on it. Torque is the rate at which angular momentum is transferred in or out of the system. When a rigid body rotates, its resistance to a change in its rotational motion is measured by its moment of inertia.

The equation for angular momentum is:

 L\ = r \times P

where  P \ is the momentum vector of the system's center of mass,  r \ is the vector from the axis of rotation to the point where the force is acting, and  \times represents the cross product of  r and  P .

Angular momentum is an important concept in both physics and engineering, with numerous applications. For example, the kinetic energy stored in a massive rotating object such as a flywheel is proportional to the square of the angular momentum.

Conservation of angular momentum also explains many phenomena in nature. The invention of the electric motor in 1860s made it possible for a gyroscope to spin indefinitely. This led to the gyrocompass, a device much used in planes and ships to stabilise movement. Inertial navigational systems for rockets were the next step.

Rotational energy[change | change source]

The rotational energy or angular kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy.

E_{rotational} = \frac{1}{2} I \omega^2


 \omega \ is the angular velocity;
 I \ is the moment of inertia (resistance to angular acceleration, equal to the product of the mass and the square of its perpendicular distance from the axis of rotation);
 E \ is the kinetic energy.

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