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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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**Title:** Conservation of Angular Momentum in Skaters

**Description:**
The diagram illustrates a scenario where twin skaters approach each other and lock hands.

**Diagram Explanation:**
- **Figure (a):** Shows the initial position where two skaters are moving towards each other with a linear velocity \( v = 1.80 \, \text{m/s} \).
- **Figure (b):** Depicts the skaters after locking hands, rotating around their center of mass with angular velocity \( \omega \).

**Problem Statement:**

**(a)** Calculate their final angular velocity in rad/s, given:
- Each skater has an initial speed of 1.80 m/s.
- Each skater has a mass of 70 kg.
- The centers of mass are 0.890 m from their locked hands.
- Approximate their moments of inertia as point masses at this radius.

**Question:** What is the angular momentum of an object moving with a linear velocity about a given point? (Provide your answer in rad/s.)

**(b)** Compare the initial and final kinetic energy.

\[
\frac{KE_i}{KE_f} = \text{?}
\]

**Explanation:** Initially, the two skaters have translational motion, while after the collision, the motion is purely rotational.

Each section challenges students to apply principles of conservation of angular momentum and energy transformation to solve real-world physics problems.
Transcribed Image Text:**Title:** Conservation of Angular Momentum in Skaters **Description:** The diagram illustrates a scenario where twin skaters approach each other and lock hands. **Diagram Explanation:** - **Figure (a):** Shows the initial position where two skaters are moving towards each other with a linear velocity \( v = 1.80 \, \text{m/s} \). - **Figure (b):** Depicts the skaters after locking hands, rotating around their center of mass with angular velocity \( \omega \). **Problem Statement:** **(a)** Calculate their final angular velocity in rad/s, given: - Each skater has an initial speed of 1.80 m/s. - Each skater has a mass of 70 kg. - The centers of mass are 0.890 m from their locked hands. - Approximate their moments of inertia as point masses at this radius. **Question:** What is the angular momentum of an object moving with a linear velocity about a given point? (Provide your answer in rad/s.) **(b)** Compare the initial and final kinetic energy. \[ \frac{KE_i}{KE_f} = \text{?} \] **Explanation:** Initially, the two skaters have translational motion, while after the collision, the motion is purely rotational. Each section challenges students to apply principles of conservation of angular momentum and energy transformation to solve real-world physics problems.
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