Angular Momentum

Angular Momentum

Angular momentum is the tendency of an object in rotational movement to continue to rotate in the absence of any interfering force. An object's momentum will not change unless it is acted upon by an outside force. When the object (or a system of objects) is spinning, other factors have to be considered in discussing the momentum of the rotational movement. This momentum is referred to as angular momentum. The principles of angular momentum applies equally to spinning objects on Earth or to orbiting objects in space.

To understand the factors of angular momentum, the various influences on rotational movement must be considered. Three of these influences are 1) the speed of points at different distances from the center of rotation (angular velocity), 2) the moment of force, a product of two vectors (also known as torque), and 3) a figure derived from the summation of the distribution of mass throughout the object and their distance from a given line (moment of inertia).

Angular velocity is defined as the rate of displacement a particular point undergoes in relation to another point over time. Using a wheel as an example, a point on the rim and a point on the axle will have completed a rotation in the same amount of time. However, the point on the rim will have gone a further distance than the point on the axle in completing the rotation. It is a property of rotational movement that speed is dependent on the distance from the center.

Torque, or rotation moment, is a product rather than a force itself. In the example of the wheel mentioned above, torque can cause the wheel to try to rotate on an axis passing through both the axle and the rim. The effect of the torque depends on where, between the center of rotation and the outermost point, the initial force is applied. The further away from the center of rotation that the torque is applied the more velocity it causes. Torque is used in reference to the product of forces that slow down or stop the object as well as those that start the object spinning.

The moment of inertia is important in the study of angular momentum because its interaction with the object's rotational velocity will never change. When the distribution of mass changes, the other factor has to compensate. When there is a reduction in the moment of inertia, then there will be a reciprocating increase in rotational velocity. The two factors always have to be balanced for the angular momentum to remain unchanged. One way the distribution of mass can changed without any loss of total mass is by a reduction in the average distance from the center of rotation. This is why a figure skater spins faster when she pulls her arms in close to her body.

Angular momentum, like all other forms of motion, follows the general principle stated in Newton's third law. In weak form, N3 says that the force of object A on object B is equal in magnitude and opposite in direction to the force of object B on A. In strong form, the forces are pictured as acting along the line joining A and B. When the force is due to an electromagnetic field, these assumptions break down; hence, electromagnetic waves can carry angular momentum.

An example of angular momentum and its conservation is given in Kepler's second law. This law states that for a planet orbiting the sun, a line from the planet to the sun sweeps across equal areas in equal times. In an elliptical orbit, as the planet moves further from the sun, it also moves slower in its orbit. The line from the Sun to the planet covers as much area when the planet moves a short distance between two points in the apogee (the most distant portion) of the ellipse as when the planet moves a greater distance at the perigee (the closest portion) of the ellipse.

Newton explained in mathematical formulations how the Sun's gravitational pull causes the planet to speed up as it gets closer to the sun and to slow down as it gets further away from the sun. The numbers associated with the speeding up and slowing down of the planet in its orbit follow the formula for the conservation of angular momentum. The statistic representing angular momentum in the formula for the Earth's orbit around the Sun does not change; neither does the mass of the object. What does change is the velocity and the radius of the ellipse. This is similar to a change in the moment of inertia for a spinning object being compensated by change in velocity, keeping angular momentum a constant.

Angular momentum is also important for scientists trying to understand subatomic physics. Since the beginning of the twentieth century, physicists have used the observed principles of angular momentum to understand the motion of particles relative to other matter in the universe (the Mach principle), the classification of certain subatomic particles by their spin, and the apparent peculiar behavior of light (sometimes it behaves like a particle, sometimes like a wave). The entire field of quantum mechanics owes much of its existence to the study of angular momentum.

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