A digital audio compact disc carries data along a continuous spiral track from the inner circumference of the disc to the outside edge. Each bit occupies 0.6 um of the track. A CD player turns t to carry the track counterclockwise above a lens at a constant speed of 1.40 m/s. (a) Find the required angular speed at the beginning of the recording where the spiral has a radius of 2.30 cm. (Enter your answer to at least one decimal place.) rad/s (b) Find the required angular speed the end of the recording, where the spiral has a radius of 4.70 cm. (Enter your answer to at least one decimal place.) rad/s (c) A full-length recording lasts for 68 min, 33 s. Find the average angular acceleration the disc. rad/s2 (d) Assuming that the acceleration constant, find the total angular displacement of the disc as it plays. rad (e) Find the total length of the track. km
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 digital audio compact disc carries data along a continuous spiral track from the inner circumference of the disc to the outside edge. Each bit occupies 0.6 μm of the track. A CD player turns the disc to carry the track counterclockwise above a lens at a constant speed of 1.40 m/s.
(a) Find the required angular speed at the beginning of the recording where the spiral has a radius of 2.30 cm. (Enter your answer to at least one decimal place.)
\[ \_\_\_\_\ \text{rad/s} \]
(b) Find the required angular speed at the end of the recording, where the spiral has a radius of 4.70 cm. (Enter your answer to at least one decimal place.)
\[ \_\_\_\_\ \text{rad/s} \]
(c) A full-length recording lasts for 68 min, 33 s. Find the average angular acceleration of the disc.
\[ \_\_\_\_\ \text{rad/s}^2 \]
(d) Assuming that the acceleration is constant, find the total angular displacement of the disc as it plays.
\[ \_\_\_\_\ \text{rad} \]
(e) Find the total length of the track.
\[ \_\_\_\_\ \text{km} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0358b5fa-6a35-4918-bb57-f6ae9ca4088e%2F505ed0f5-0c99-47f5-a0d5-e812d4fd873f%2Fi0uk5zi_processed.jpeg&w=3840&q=75)
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