Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
Diane sits on a piano stool that rotates freely. She is holding 2 kg masses in each hand of her outstretched arms. The moment of inertia of Diane, the piano bench and the masses is 7.2 kg x m^2 and the stool is rotating at a constant angular speed of 1.2 rev/s. Diane then brings her arms in close to her body and in doing so changes the moment of inertia to 5.5 kg x m^2.
(a) What is the new rotational speed of the bench?
(b) Calculate the ratio of the new kinetic energy of the rotating system to the original kinetic energy.
(c) What provided the added kinetic energy?
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