5. Two particles, each with m = 0.5 kg, are fastened to each other to a rotation axis at O, by two massless rods, each with length d = 6 cm. a. What is the moment of inertia of the system? b. If the angular position of the system is given by 0 = 2t³ — t² + 3, find the angular velocity of the rotating system at t = 2.0 s. c. Find the kinetic energy of the system at t = 2.0 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)...
icon
Related questions
Question
**Problem 5: Rotational Motion of a Two-Particle System**

Two particles, each with mass \( m = 0.5 \, \text{kg} \), are fastened to each other and to a rotation axis at point \( O \) by two massless rods, each with a length \( d = 6 \, \text{cm} \).

**Questions:**

a. What is the moment of inertia of the system?

b. If the angular position of the system is given by \(\theta = 2t^3 - t^2 + 3\), find the angular velocity of the rotating system at \( t = 2.0 \, \text{s} \).

c. Find the kinetic energy of the system at \( t = 2.0 \, \text{s} \).

**Answers:**

- Moment of Inertia: \( I = 9 \times 10^{-3} \, \text{kg} \, \text{m}^2 \)
- Angular Velocity: \( \omega = 20 \, \text{rad/s} \)
- Kinetic Energy: \( K_E = 1.8 \, \text{J} \)

**Diagram Explanation:**

The diagram shows:

- A rotation axis at point \( O \).
- Two particles, each at the end of a rod of length \( d \).
- The particles are highlighted in blue.
- An arrow represents the angular velocity (\(\omega\)), indicating the direction of rotation.
Transcribed Image Text:**Problem 5: Rotational Motion of a Two-Particle System** Two particles, each with mass \( m = 0.5 \, \text{kg} \), are fastened to each other and to a rotation axis at point \( O \) by two massless rods, each with a length \( d = 6 \, \text{cm} \). **Questions:** a. What is the moment of inertia of the system? b. If the angular position of the system is given by \(\theta = 2t^3 - t^2 + 3\), find the angular velocity of the rotating system at \( t = 2.0 \, \text{s} \). c. Find the kinetic energy of the system at \( t = 2.0 \, \text{s} \). **Answers:** - Moment of Inertia: \( I = 9 \times 10^{-3} \, \text{kg} \, \text{m}^2 \) - Angular Velocity: \( \omega = 20 \, \text{rad/s} \) - Kinetic Energy: \( K_E = 1.8 \, \text{J} \) **Diagram Explanation:** The diagram shows: - A rotation axis at point \( O \). - Two particles, each at the end of a rod of length \( d \). - The particles are highlighted in blue. - An arrow represents the angular velocity (\(\omega\)), indicating the direction of rotation.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Torque
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON