•• P34 A sphere or cylinder of mass M, radius R, and moment of inertia I rolls without slipping down a hill of height h, starting from rest. As explained in Problem P33, if there is no slipping w = vcM/R. (a) In terms of the given variables (M, R, I, and h), what is v, (c) If the object is a uniform-density solid cylinder, what is vy at the bottom of the hill? (d) If the object is a uniform-density sphere, what is vay at the bottom of the hill? An interesting experiment that you can perform is to roll various objects down CM at the bottom of the hill? (b) If the object is a thin hollow cylinder, what is v, CM at the bottom of the hill? an inclined board and see how much time each one takes to reach the bottom.
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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