A person of mass m = 75 kg stands in the center of a large rotating disk with radius R= 5.0 m and total mass M. The rotates without friction and without any external torque, initially at an angular velocity of w. The moment of inertia of a disk is MR. Assume that the can be approximated as point-like, i.e. the angular momentum is r x p. The person then walks radially outward. person (a) What is the angular momentum of the system (person + disk) as a function of the person's radius, r, from the center? Write it in terms of m, M, R, and w. (b) If the disk is initially rotating at wo and it slows to wf = 0.8 rad/s when the person is at the very edge, what is the mass of the disk? 1.1 rad/s when the person is in the exact center, %3D (c) What is the rotational kinetic energy of the system before and after the person walks to the edge?
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.
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