A uniform, solid, 100-kg cylinder with a diameter of 1.0 m is mounted so it is free to rotate about fixed, horizontal, frictionless axis that passes through the centers of its circular ends. A 10-kg block is hung from a very light thin cord wrapped around the cylinder's circumference When the block is released, the cord unwinds and the block accelerates downward, as shown in the figure. What is the acceleration of the block? m/s²
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.
![**Physics Problem: Rotational Motion and Acceleration**
A uniform, solid, 100-kg cylinder with a diameter of 1.0 m is mounted so it is free to rotate about a fixed, horizontal, frictionless axis that passes through the centers of its circular ends. A 10-kg block is hung from a very light, thin cord wrapped around the cylinder's circumference.
*Diagram Description:* The diagram shows a cylinder with a thin cord wrapped around it. A block is hanging from the cord. The cylinder is mounted horizontally and can rotate freely about its central axis.
**Problem Statement:**
When the block is released, the cord unwinds, and the block accelerates downward, as depicted in the figure.
**Question:**
What is the acceleration of the block?
\[ \text{Acceleration of the block} = \quad \text{__________} \quad \text{m/s}^2 \]
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**Explanation:**
To solve for the acceleration of the block, we need to consider both the rotational motion of the cylinder and the linear motion of the block. This involves applying Newton's second law for rotational motion and linear motion, as well as the relationship between the linear acceleration of the block and the angular acceleration of the cylinder.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f7775f3-edad-4f27-ba1b-f7886a7505bd%2Feb5f4ce1-91db-4446-8fa2-20413ef1bcbe%2Fq9m11ep_processed.jpeg&w=3840&q=75)
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