A uniform rod of mass 2.20 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 5.30 kg is attached to one end and a second mass m2 = 2.20 kg is attached to the other end of the rod. Treat the two masses as point particles.(a)What is the moment of inertia of the system in kg · m2? kg · m2(b)If the rod rotates with an angular speed of 2.70 rad/s, how much kinetic energy, in joules, does the system have? J(c)Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined, in kg · m2? kg · m2(d)If the rod is of negligible mass, what is the kinetic energy, in joules, when the angular speed is 2.70 rad/s? J The image depicts a two-body system consisting of two masses, \( m_1 \) and \( m_2 \), connected by a rod of length \( \ell \). This system is undergoing rotational motion around a central point, with the masses moving in a circular path.### Features of the Diagram:- **Masses**: - \( m_1 \): A sphere colored in purple. - \( m_2 \): A sphere colored in red.- **Rod**: The two masses are connected by a straight rod (gray) of length \( \ell \).- **Axes**: - The diagram includes an x-axis and a y-axis, with the origin at the center of rotation.- **Circular Path**: - The system's motion traces a dashed circular path, indicating rotation about the central point.- **Velocity Vectors**: - Two green arrows labeled \( \vec{v} \) indicate the direction of velocity for each mass. These vectors are tangential to the circular path of rotation.- **Angles**: - The diagram shows the angles formed by each velocity vector with respect to the radial line connecting the center of the circle to each mass, representing the tangential nature of the velocity in circular motion.This illustration is typically used to explain concepts like rotational motion, angular velocity, and centripetal force in physics.

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Answered: A uniform rod of mass 2.20 kg and…

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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A uniform rod of mass 2.20 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass

m₁ = 5.30 kg

is attached to one end and a second mass

m₂ = 2.20 kg

is attached to the other end of the rod. Treat the two masses as point particles.

(a)

What is the moment of inertia of the system in kg · m²?

kg · m²

(b)

If the rod rotates with an angular speed of 2.70 rad/s, how much kinetic energy, in joules, does the system have?

(c)

Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined, in kg · m²?

kg · m²

(d)

If the rod is of negligible mass, what is the kinetic energy, in joules, when the angular speed is 2.70 rad/s?

The image depicts a two-body system consisting of two masses, \( m_1 \) and \( m_2 \), connected by a rod of length \( \ell \). This system is undergoing rotational motion around a central point, with the masses moving in a circular path.

### Features of the Diagram:

- **Masses**:
- \( m_1 \): A sphere colored in purple.
- \( m_2 \): A sphere colored in red.

- **Rod**: The two masses are connected by a straight rod (gray) of length \( \ell \).

- **Axes**:
- The diagram includes an x-axis and a y-axis, with the origin at the center of rotation.

- **Circular Path**:
- The system's motion traces a dashed circular path, indicating rotation about the central point.

- **Velocity Vectors**:
- Two green arrows labeled \( \vec{v} \) indicate the direction of velocity for each mass. These vectors are tangential to the circular path of rotation.

- **Angles**:
- The diagram shows the angles formed by each velocity vector with respect to the radial line connecting the center of the circle to each mass, representing the tangential nature of the velocity in circular motion.

This illustration is typically used to explain concepts like rotational motion, angular velocity, and centripetal force in physics.

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