A disk rotates about an axis through its center. Point A is located on its rim and point B is located exactly one fifth of the way from the center toward the rim. What is the ratio of the angular velocity w, to that of wg, and the tangential velocity va to that of vg? HINT (a) the angular velocity Wa to that of wB (b) the tangential velocity va to that of ve VA
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.
![**Rotational Motion of a Disk**
A disk rotates about an axis through its center. Point A is located on its rim, while point B is positioned exactly one fifth of the way from the center toward the rim. This problem asks for the ratio of the angular velocity \(\omega_A\) at point A to that of \(\omega_B\) at point B, and similarly, the ratio of the tangential velocity \(v_A\) at point A to that of \(v_B\) at point B.
**HINT**: Understand the relationships between angular velocity and tangential velocity at different points on the rotating disk.
**(a)** Determine the ratio of the angular velocity at point A to that at point B.
\[
\frac{\omega_A}{\omega_B} =
\]
**(b)** Determine the ratio of the tangential velocity at point A to that at point B.
\[
\frac{v_A}{v_B} =
\]
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Note: This explanation is designed to help you apply principles of rotational motion to calculate the requested ratios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6908594-6723-4553-b0f8-d60d771be678%2F0d4b0700-d41c-4107-8694-d2c62564a031%2Fsfdhb03_processed.jpeg&w=3840&q=75)
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