A block (mass = 1.1 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.2 x 103 kg-m²), as the figure shows. Initially the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord 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 0.042 m during the block's descent. Find (a) the angular acceleration of the pulley and (b) the tension in the cord.
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.
![**Problem Statement:**
A block (mass = 1.1 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = \(1.2 \times 10^{-3} \, \text{kg} \cdot \text{m}^2\)), as the figure shows. Initially, the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord 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 0.042 m during the block's descent. Find (a) the angular acceleration of the pulley and (b) the tension in the cord.
**Diagram Description:**
A simple diagram depicts a pulley fixed on a horizontal support with a cord wrapped around it. A block is hanging from the cord under the pulley. The cord remains taut as the block descends.
**Questions:**
(a) Angular acceleration of the pulley
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(b) Tension in the cord
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