the motion of this rolling package. You múst use all of the following terms: trans- lational motion, rotational motion, angular velocity, angular momentum, torque.
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.
The laws and equations that govern nature and natural phenomena are described by physics. One prime focus of physics is the study of motion. The rolling motion is a combination of translational motion and rotational motion. For a body, the motion of the center of mass is the translational motion of the body. During the rolling motion of a body, the surfaces in contact get deformed a little temporarily. Due to this deformation, a finite area of both bodies comes in contact with each other. The overall effect of this phenomenon is that the component of the contact force parallel to the surface opposes motion resulting in friction.
Let vcm is the velocity of the center of mass of a disc-shaped body. Since for a rolling disc, the center of mass would lie at the geometric center C, the velocity of body or velocity of C is vcm which is parallel to the rolling surface. The rotational motion of the body occurs about its axis of symmetry, therefore, the velocity at any point P0, P1, or P2 of the body comprises two parts, translational velocity vcm, and due to rotational motion, it has linear velocity vr, where vr=r. is the angular velocity of the rolling disc. vr is perpendicular to the radius vector at any point lying on the disc with respect to the geometric center C. Consider the point P0 on the disc. vr is directed opposite to vcm and at this point vr=R, where R is the radius of the disc. Therefore, for the disc, the condition for rolling without slipping is given by vcm=R. The kinetic energy of such a rolling body is given by the sum of kinetic energies of translational motion and rotation which is as follows:-
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