### Problem:Suppose the particles shown below have masses \( m_1 = 0.18 \, \text{kg} \), \( m_2 = 0.36 \, \text{kg} \), \( m_3 = 0.54 \, \text{kg} \), \( m_4 = 0.72 \, \text{kg} \). The velocities of the particles are \( \mathbf{v_1} = 3.5 \hat{\mathbf{i}} \, \text{m/s} \), \( \mathbf{v_2} = (5.3 \hat{\mathbf{i}} - 5.3 \hat{\mathbf{j}}) \, \text{m/s} \), \( \mathbf{v_3} = -2.6 \hat{\mathbf{j}} \, \text{m/s} \), \( \mathbf{v_4} = -7.0 \hat{\mathbf{i}} \, \text{m/s} \). (Express your answers in vector form.)#### Diagram Explanation:The diagram shows four particles in an xy-coordinate plane:- Particle \( m_1 \) is located at (0, 2) with velocity \( \mathbf{v_1} \).- Particle \( m_2 \) is located at (2, -4) with velocity \( \mathbf{v_2} \).- Particle \( m_3 \) is located at (-4, -2) with velocity \( \mathbf{v_3} \).- Particle \( m_4 \) is located at (4, 0) with velocity \( \mathbf{v_4} \).### Tasks:(a) Calculate the angular momentum of each particle about the origin (in \( \text{kg} \cdot \text{m}^2/\text{s} \)).\[\begin{align*}\vec{L}_1 &= \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \text{kg} \cdot \text{m}^2/\text{s} \\\vec{L}_2 &= \, \, \, \, \, \, \, \

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Suppose the particles shown below have masses m, = 0.18 kg, m, = 0.36 kg, m, = 0.54 kg, m, = 0.72 kg. The velocities of the particles are v, = 3.5Î m/s, v, = (5.3î – 5.3j) m/s, vą = -2.6j m/s, V, = -7.0î m/s. (Express your answers in vector form.) y(m)4 4.0 m, 2.0 m2 m4 -4.0 -2.0 2.0 4.0 x(m) -2.0- m2. -4.0- V2 (a) Calculate the angular momentum of each particle about the origin (in kg • m2/s). ī, = kg • m?/s ī, = kg - m?/s kg · m2/s kg - m2/s (b) What is the total angular momentum of the four-particle system about the origin (in kg · m2/s)? L= kg - m?/s

Suppose the particles shown below have masses m, = 0.18 kg, m, = 0.36 kg, m, = 0.54 kg, m, = 0.72 kg. The velocities of the particles are v, = 3.5Î m/s, v, = (5.3î – 5.3j) m/s, vą = -2.6j m/s, V, = -7.0î m/s. (Express your answers in vector form.) y(m)4 4.0 m, 2.0 m2 m4 -4.0 -2.0 2.0 4.0 x(m) -2.0- m2. -4.0- V2 (a) Calculate the angular momentum of each particle about the origin (in kg • m2/s). ī, = kg • m?/s ī, = kg - m?/s kg · m2/s kg - m2/s (b) What is the total angular momentum of the four-particle system about the origin (in kg · m2/s)? L= kg - m?/s

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.

Question

### Problem:

Suppose the particles shown below have masses \( m_1 = 0.18 \, \text{kg} \), \( m_2 = 0.36 \, \text{kg} \), \( m_3 = 0.54 \, \text{kg} \), \( m_4 = 0.72 \, \text{kg} \). The velocities of the particles are \( \mathbf{v_1} = 3.5 \hat{\mathbf{i}} \, \text{m/s} \), \( \mathbf{v_2} = (5.3 \hat{\mathbf{i}} - 5.3 \hat{\mathbf{j}}) \, \text{m/s} \), \( \mathbf{v_3} = -2.6 \hat{\mathbf{j}} \, \text{m/s} \), \( \mathbf{v_4} = -7.0 \hat{\mathbf{i}} \, \text{m/s} \). (Express your answers in vector form.)

#### Diagram Explanation:

The diagram shows four particles in an xy-coordinate plane:

- Particle \( m_1 \) is located at (0, 2) with velocity \( \mathbf{v_1} \).
- Particle \( m_2 \) is located at (2, -4) with velocity \( \mathbf{v_2} \).
- Particle \( m_3 \) is located at (-4, -2) with velocity \( \mathbf{v_3} \).
- Particle \( m_4 \) is located at (4, 0) with velocity \( \mathbf{v_4} \).

### Tasks:

(a) Calculate the angular momentum of each particle about the origin (in \( \text{kg} \cdot \text{m}^2/\text{s} \)).

\[
\begin{align*}
\vec{L}_1 &= \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \text{kg} \cdot \text{m}^2/\text{s} \\
\vec{L}_2 &= \, \, \, \, \, \, \, \

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