Momentum and Angular momentum

Ordinary momentum is a measure of an object's tendency to move at constant speed along a straight path. Momentum depends on speed and mass. A train moving at 20 mph has more momentum than a bicyclist moving at the same speed. A car colliding at 5 mph does not cause as much damage as that same car colliding at 60 mph. For things moving in straight lines:

momentum= mass speed

When things move in curved paths, the idea of momentum can be generalized as angular momentum. Angular momentum measures an object's tendency to continue to spin or, in other words, the angular momentum is the physical quantity which describes the dynamics of objects that are spinning or revolving round an axis. An ``object'' can be either a single body or two or more bodies acting together as a single group. The angular momentum is normally defined as:

angular momentum = mass velocity distance (from the point object is spinning or orbiting around)

Let's suppose the object (or group of objects) has no outside forces acting on it (in a way to produce torques that would disturb the angular motion of the object). In these cases, we have conservation of angular momentum.

This means that the total amount of angular momentum does not change with time no matter how the objects interact with one another.


A simple example:
the angular momentum L of a dumbbell (two masses m, connected by a massless bar of length d) freely spinning on a plane with angular velocity w around the axis perpendicular to this plane and passing through the center of the bar, is computed as:

Since the dumbbell is a free spinning body, L is conserved. If, for a particular reason, the distance d changes, the angular velocity must change according to equation:

Hence, if d becomes smaller, the dumbbell must spin faster. This is, for example, the reason why an ice-skater spins faster when she keeps her arms closer to her body!!



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