1. A uniform rod of length L and mass 2m is free to rotate on a frictionless pin through its center of mass. At the end of rod on each side, there is a ball of radius 1/5 L and mass m attached to it. The system (rod+balls) is initially at rest in a horizontal position. A piece of clay of mass m/10 drops from a height h meters above the center of one of the ball, and sticks to the ball after the collision. Find (a) the rotational inertia of the ball-rod-ball system before the collision. (b) the angular velocity and angular acceleration of the system (ball-rod-ball plus the clay) right after the collision. 2 < clay
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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