College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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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.
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