I. A hollow ball of mass M and radius R is released from rest at the top of a bumpy track. The starting point is at height H from the bottom and the top of the bump is at height 2H/3 from the bottom of the track, as shown in Fig.1. Over the entire course of its motion, the ball rolls without slipping. The acceleration due to gravity has magnitude g and air resistance is negligible. a. Explain which physical quantity (ies) is (are) conserved over the course of the displacement of the ball along the track. b.Determine the linear speed of the ball at the lowest point on the track. c. Determine which fraction of the mechanical energy of the ball its rotational kinetic energy represents when it reaches the top of the bump.
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.
QI. A hollow ball of mass M and radius R is released from rest at the top of a bumpy track. The starting point is at height H from the bottom and the top of the bump is at height 2H/3 from the bottom of the track, as shown in Fig.1. Over the entire course of its motion, the ball rolls without slipping. The acceleration due to gravity has magnitude g and air resistance is negligible.
a. Explain which physical quantity (ies) is (are) conserved over the course of the displacement of the ball along the track.
b.Determine the linear speed of the ball at the lowest point on the track.
c. Determine which fraction of the mechanical energy of the ball its rotational kinetic energy represents when it reaches the top of the bump.
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