The same force F is applied to the edge of 2 hoops, as shown. Bother have the same uniform mass except, the larger hoop has twice the radius as the smaller. Which hoop experiences the greater torque, and how much more? 2R R Axis day Axis Mass = M Mass = M %3D %3D O The larger hoop, 2 times larger The smaller hoop, 2 times larger O The smaller hoop, 4 times larger O The larger hoop, 4.times larger O Both hoops have the same
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.
![The image presents a physics problem involving two hoops. Here's the transcription and explanation suitable for an educational context:
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**Problem Statement:**
The same force \( F \) is applied to the edge of two hoops, as shown. Both hoops have the same uniform mass except the larger hoop has twice the radius of the smaller one. Which hoop experiences the greater torque, and how much more?
**Diagrams:**
- **Diagram of Two Hoops:**
- The smaller hoop has a radius \( R \) and mass \( M \).
- The larger hoop has a radius \( 2R \) and mass \( M \).
- The force \( F \) is applied tangentially to both hoops.
**Options:**
- ○ The larger hoop, 2 times larger
- ○ The smaller hoop, 2 times larger
- ○ The smaller hoop, 4 times larger
- ○ The larger hoop, 4 times larger
- ○ Both hoops have the same
**Analysis:**
Torque (\( \tau \)) is calculated using the formula:
\[ \tau = R \times F \]
Since the force \( F \) is the same for both hoops, the torque is directly proportional to the radius.
- **Torque of the smaller hoop:**
\[ \tau_{\text{small}} = R \times F \]
- **Torque of the larger hoop:**
\[ \tau_{\text{large}} = 2R \times F \]
Thus, the torque on the larger hoop is twice as large as the torque on the smaller hoop.
The correct answer would be **"The larger hoop, 2 times larger."**
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This explanation details how to understand torque application in physics by observing how the radius influences it when a constant force is applied.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc498df87-f430-40e5-873e-319addd6a9d3%2F2116419f-b07e-4946-a00e-f7f58cd5dedb%2Fk6xixhr.jpeg&w=3840&q=75)
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