A disk is free to rotate about an axis through its center. The radius of the disk is 0.1 m and its mass is 6 kg. Three forces are acting on the disk as shown in the figure below. The disk is rotating at 100 rpm. Use this information to answer the next 7 questions. 5N 10 N 1N
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 Concepts and Applications: Moments of Inertia and Angular Motion
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#### Question 4
**What is the moment of inertia of the disk?**
- [ ] \(0.83 \, \text{kg} \cdot \text{m}^2 \)
- [ ] \(0.023 \, \text{kg} \cdot \text{m}^2 \)
- [ ] \(0.68 \, \text{kg} \cdot \text{m}^2 \)
- [ ] \(2.1 \, \text{kg} \cdot \text{m}^2 \)
- [ ] \(1.18 \, \text{kg} \cdot \text{m}^2 \)
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#### Question 5
**What is the magnitude of the angular acceleration of the disk?**
- [ ] \(8 \, \text{rad/s}^2\)
- [ ] \(120 \, \text{rad/s}^2\)
- [ ] \(42 \, \text{rad/s}^2\)
- [ ] \(100 \, \text{rad/s}^2\)
- [ ] \(20 \, \text{rad/s}^2\)
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#### Question 6
**Suppose that a ball of clay (mass \(m\)) falls onto the edge of the disk (mass \(M\), radius \(R\)) and sticks. What is the moment of inertia of the disk + clay system?**
- [ ] \(I = MR^2\)
- [ ] \(I = \frac{1}{2}MR^2 + mR^2\)
- [ ] \(I = \frac{3}{2}MR^2 + mR^2\)
- [ ] \(I = 2mR^2\)
- [ ] \(I = \frac{1}{2}MR^2 - mR^2\)
- [ ] \(I = mR^2\)
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#### Question 7
**Suppose the mass of the clay that falls onto the disk is 2 kg. What is the angular speed of the disk after the clay is added? You can leave your answer in rpm.**
- [ ] 0 rpm
- [ ] 45 rpm
- [ ] 90 rpm
- [ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F072e444d-1bde-4899-b3c3-9f07885f3d58%2Fc71a5755-cf3f-4d56-8c3d-5901c961a0c5%2Figx5szt_processed.png&w=3840&q=75)
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