A light rigid rod of length = 1.00 m in length rotates about an axis perpendicular to its length and through its center, as shown in the figure below. Two particles of masses m₁ = 4.70 kg and m₂ = 3.00 kg are connected to the ends of the rod. What is the angular momentum of the system if the speed of each particle is 5.50 m/s? (Neglect the rod's mass.) J.S m₁ Mg
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.
![**Problem Statement:**
A light rigid rod of length \( \ell = 1.00 \, \text{m} \) rotates about an axis perpendicular to its length and through its center, as shown in the figure below. Two particles of masses \( m_1 = 4.70 \, \text{kg} \) and \( m_2 = 3.00 \, \text{kg} \) are connected to the ends of the rod. What is the angular momentum of the system if the speed of each particle is \( 5.50 \, \text{m/s} \)? (Neglect the rod's mass.)
[Input field for answer] \( \, \text{J} \cdot \text{s} \)
**Diagram Explanation:**
- The diagram shows a horizontal rod along the x-axis, with red arrows pointing tangentially in opposite directions indicating the motion of masses \( m_1 \) and \( m_2 \).
- The mass \( m_1 \) is depicted on the negative x-axis, and the mass \( m_2 \) is on the positive x-axis.
- Both masses are rotating in a circular path around the center of the rod.
- The dashed line represents the circular path of rotation around the center.
- The rotation axis is shown as a small circle at the center of the rod on the intersection of the x and y axes.
**To calculate the angular momentum \( L \) of the system:**
1. Find the linear momentum of each mass:
- \( p_1 = m_1 \times v = 4.70 \, \text{kg} \times 5.50 \, \text{m/s} \)
- \( p_2 = m_2 \times v = 3.00 \, \text{kg} \times 5.50 \, \text{m/s} \)
2. Calculate the angular momentum for each mass:
- \( L_1 = r_1 \times p_1 = (\ell/2) \times p_1 = (1.00 \, \text{m}/2) \times p_1 \)
- \( L_2 = r_2 \times p_2 = (\ell/2) \times p_2 = (1.00 \, \text{m}/2) \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84f39a0e-1c16-43ec-bcb3-7f889ca233a2%2F0015abad-ea70-4413-a552-e92c525e0b0b%2Fjlfgygf_processed.png&w=3840&q=75)
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