Twin skaters approach one another as shown in the figure below and lock hands. (a) (b) (a) Calculate their final angular velocity in rad/s, given each had an initial speed of 1.80 m/s relative to the ice. Each has a mass of 70 kg, and their centers of mass are 0.890 m from their locked hands. You may approximate their moments of inertia to be that of point masses at this radius. X What is the angular momentum of an object moving with a linear velocity about a given point? rad/s (b) Compare the initial and final kinetic energy. KE₁ KEf Initially the two skaters have translational motion while after the collision it is purely rotational. X

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### Twin Skaters Problem

Twin skaters approach one another as shown in the figure and lock hands.

#### Figure Explanation
- **Diagram (a):** Shows two skaters moving toward each other with linear velocity \(v = 1.80 \, \text{m/s}\).
- **Diagram (b):** Illustrates the skaters after locking hands and rotating with angular velocity \(\omega\).

### Problem Statement

**(a)** Calculate their final angular velocity \(\omega\) in rad/s. Each skater has:
- An initial speed of \(1.80 \, \text{m/s}\).
- A mass of \(70 \, \text{kg}\).
- Centers of mass \(0.890 \, \text{m}\) from their locked hands.

Approximate their moments of inertia as point masses at this radius.

- **Prompt Question:** What is the angular momentum of an object moving with a linear velocity about a given point? (Answer in rad/s)

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

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

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

This exercise demonstrates concepts of conservation of angular momentum and kinetic energy transformation.
Transcribed Image Text:### Twin Skaters Problem Twin skaters approach one another as shown in the figure and lock hands. #### Figure Explanation - **Diagram (a):** Shows two skaters moving toward each other with linear velocity \(v = 1.80 \, \text{m/s}\). - **Diagram (b):** Illustrates the skaters after locking hands and rotating with angular velocity \(\omega\). ### Problem Statement **(a)** Calculate their final angular velocity \(\omega\) in rad/s. Each skater has: - An initial speed of \(1.80 \, \text{m/s}\). - A mass of \(70 \, \text{kg}\). - Centers of mass \(0.890 \, \text{m}\) from their locked hands. Approximate their moments of inertia as point masses at this radius. - **Prompt Question:** What is the angular momentum of an object moving with a linear velocity about a given point? (Answer in rad/s) **(b)** Compare the initial and final kinetic energy. \[ \frac{KE_i}{KE_f} = \] - **Prompt Explanation:** Initially, the two skaters have translational motion, while after the collision, it is purely rotational. This exercise demonstrates concepts of conservation of angular momentum and kinetic energy transformation.
Expert Solution
Step 1

Solution:

Given:

m = mass of each skater = 70 kg

v = initial speed of each skater = 1.80 m/s

r = distance between their centre of mass and locked hands = 0.890 m

ω = final angular velocity = ?

KEi = initial kinetic energy of system

KEf = final kinetic energy of system

R = ratio of KEiKEf= ? 

 

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