The moment of inertia of a thin spherical shell of mass M and radius R about an axis through its center is given by I =MR? In a "trick shot", a ping pong ball of mass 2.7 grams and radius 2cm is released at rest from the top of a curved track. The curved track becomes horizontal at the end, as shown. The ping pong ball rolls without slipping along the track. The objective is to have the ping pong ball ultimately fall into the cup shown. Use the heights indicated in the figure and neglect work done by friction and air resistance. (a) Find the linear speed attained by the ping pong ball when it reaches the end of the track (since the track becomes horizontal at the end, the velocity at that point is also horizontally directed). (b) Hence, find d, the horizontal distance from the end of track at which the cup must be kept such that the ping pong ball falls into it. .
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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