College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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**Problem 6: Rotational Motion**

A wheel has a radius of 0.15 m and a moment of inertia of 4.00 kg·m². It starts from rest and accelerates under a constant torque of 12.0 N·m for 4.00 seconds.

a. **What is the wheel’s angular acceleration?**

b. **What is the wheel’s angular velocity at the end of 4.00 s?**

c. **What is the linear velocity of the edge of the wheel after 4 s?**

---

**Explanation:**

- **Angular Acceleration (a):** Calculated using the formula \(\alpha = \frac{\tau}{I}\), where \(\tau\) is the torque and \(I\) is the moment of inertia.
  
- **Angular Velocity (b):** Determined after 4 seconds using \(\omega = \alpha t\), assuming initial angular velocity is zero.
  
- **Linear Velocity (c):** Found using the relationship \(v = \omega r\), where \(r\) is the radius of the wheel.
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Transcribed Image Text:**Problem 6: Rotational Motion** A wheel has a radius of 0.15 m and a moment of inertia of 4.00 kg·m². It starts from rest and accelerates under a constant torque of 12.0 N·m for 4.00 seconds. a. **What is the wheel’s angular acceleration?** b. **What is the wheel’s angular velocity at the end of 4.00 s?** c. **What is the linear velocity of the edge of the wheel after 4 s?** --- **Explanation:** - **Angular Acceleration (a):** Calculated using the formula \(\alpha = \frac{\tau}{I}\), where \(\tau\) is the torque and \(I\) is the moment of inertia. - **Angular Velocity (b):** Determined after 4 seconds using \(\omega = \alpha t\), assuming initial angular velocity is zero. - **Linear Velocity (c):** Found using the relationship \(v = \omega r\), where \(r\) is the radius of the wheel.
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