The figure shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance of d = 0.837 m, and rotating with an angular speed of 102 rad/s. The bullet first passes through the left disk and then through the right disk. It is found that the angular displacement between the two bullet holes is A = 0.211 rad. From these data, determine the speed of the bullet. Bullet Mator Number Units
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.
![### Measuring the Speed of a Bullet Using Rotating Disks
The figure illustrates a device designed for measuring the speed of a bullet. The setup includes two rotating disks, which are positioned a distance \(d = 0.837 \, \text{m}\) apart. These disks rotate with an angular speed of \(102 \, \text{rad/s}\).
### Concept and Measurement Process
1. **Initial Bullet Pass Through**: As the bullet travels, it first penetrates the left disk.
2. **Subsequent Bullet Pass Through**: The bullet then continues its trajectory through to the right disk.
3. **Determining Angular Displacement**: The device measures the angular displacement between the two bullet holes in the disks, denoted by \(\theta = 0.211 \, \text{rad}\).
### Calculation to Determine Bullet Speed
From these collected data points, we aim to determine the speed of the bullet. The calculation is based on the relationship between the distance of separation \(d\), the angular speed \(\omega\), and the angular displacement \(\theta\).
### Diagram Explanation
The diagram accompanying this setup:
- **Motor and Rotating Disks**: Shows a motor driving two disks at a constant angular speed.
- The left disk is where the bullet first passes through, continuing to the right disk.
- **Distance \(d\) of Separation**: The separation distance \(d\) between the disks is clearly labeled.
- **Bullet Path**: The trajectory of the bullet, allowing the calculation of the bullet’s speed after passing through both disks.
### Calculation Formula
To calculate the speed of the bullet (\(v\)), the following formula can be used:
\[
v = \frac{d \cdot \omega}{\theta}
\]
Where:
- \(d = 0.837 \, \text{m}\) (distance between the disks)
- \(\omega = 102 \, \text{rad/s}\) (angular speed of disks)
- \(\theta = 0.211 \, \text{rad}\) (angular displacement)
Fill in the values and perform the calculation to find the bullet's speed.
### Interactive Section
Below this explanation, there is an interactive part where students can input the necessary values (number and units) to calculate the desired speed of the bullet.
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This educational setup allows students to understand the principles of rotational motion and angular](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0799116-775e-49f7-a375-632b56bcacd3%2F51f8efc0-d1d9-4ac9-956b-4365392e4512%2Fz4i40j_processed.jpeg&w=3840&q=75)
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