A block (mass -3.0 kg) is hanging from a mass-less string that is wrapped around a pulley (moment of inertia - 1.3x10 kg.m² ). The string is 120 cm long. Initially the string was wrapped fully and the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The string does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.050 m during the block's descent. The mass rolls from rest down to the end of the string. (d) transnational kinetic energy (e) rotational kinetic energy, (f) angular speed (g) angular momentum
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.
A block (mass = 3.0kg) is hanging from a mass-less string that is wrapped around a pulley. The string is 120cm long. Initially the string was wrapped fully and the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.050m during the block's descent. The mass rolls from rest down to the end of the string.
Find the transnational kinetic energy.
Find the rotational kinetic energy.
Find the angular speed.
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