The angular velocity of an object is a measure of how fast it is spinning. It is represented by the
Greek letter omega, written w, (not to be confused with the letter w which, unlike omega, is
pointed on the bottom). The most convenient measure of angle in discussing rotational motion is
the radian. Like the degree, a radian is a fraction of a revolution. But, while one degree is 1 of
360
a revolution, one radian is 1 of a revolution. The units of angular velocity are then radians per
2π
rad
second or, in notational form,
. Angular velocity has direction or sense of rotation
s
associated with it. If one defines a rotation which is clockwise when viewed from above as a
positive rotation, then an object which is rotating counterclockwise as viewed from above is said
to have a negative angular velocity. In any problem involving angular velocity, one is free to
choose the positive sense of rotation, but then one must stick with that choice throughout the
problem.
Angular Momentum
The angular momentum L of an object is given by:
L = Iw (5-1)
Note that this is consistent with our original definition of angular momentum as a measure of the
degree of the object's tendency to keep on spinning, once it is spinning. The greater the
rotational inertia of the object, the more difficult it is to stop the object from spinning, and the
greater the angular velocity of the object, the more difficult it is to stop the object from spinning.
The direction of angular momentum is the same as the direction of the corresponding angular
velocity.
Torque
We define torque by analogy with force which is an ongoing push or pull on an object. When
there is a single force acting on a particle, the momentum of that particle is changing. A torque
is what you are exerting on the lid of a jar when you are trying to remove the lid. When there is
a single torque acting on a rigid object, the angular momentum of that object is changing.
Conservation of Angular Momentum
Angular Momentum is an important concept because, if there is no angular momentum
transferred to or from a system, the total angular momentum of that system does not change, and
if there is angular momentum being transferred to a system, the rate of change of the angular
momentum of the system is equal to the rate at which angular momentum is being transferred to
the system. As in the case of energy and momentum, this means we can use simple accounting
(bookkeeping) procedures for making predictions on the outcomes of physical processes. In this
chapter we focus on the special case in which there are no external torques which means that no
angular momentum is transferred to or from the system.
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