help **Topic: Rotational Kinetic Energy****Problem:**Calculate the rotational kinetic energy of a spinning (not rolling) bowling ball with a mass of 12 kg, a radius of 0.20 m, and a velocity of 5 m/s.*Fun Fact: How can this problem be solved if the radius (r) isn't provided?***Key Formulas and Concepts:**1. **Relationship Between Linear and Angular Velocity:** - \( v = r\omega \) - Where \( v \) is linear velocity, \( r \) is radius, and \( \omega \) is angular velocity.2. **Moment of Inertia (I) for Various Shapes:** - **Sphere:** \( I_{\text{sphere}} = \frac{2}{5} MR^2 \) - **Cylinder:** \( I_{\text{cylinder}} = \frac{1}{2} MR^2 \) - **Ring:** \( I_{\text{ring}} = MR^2 \) - **Stick (through center):** \( I_{\text{stick thru center}} = \frac{1}{12} ML^2 \) - **Stick (through end):** \( I_{\text{stick thru end}} = \frac{1}{3} ML^2 \)These equations allow calculation of the rotational kinetic energy using appropriate moment of inertia for the object's shape. The bowling ball in this instance is modeled as a sphere.

mass of bowling ball (m) = 12 kg Radius of ball (r) = 0.20 m Velocity (v) = 5 m/s

Answered: Find the rotational kinetic energy of a…

Find the rotational kinetic energy of a spinning (not rolling) bowling ball that has a mass of 12 kg and a radius of 0.20 m moving at 5 m/s. (Fun fact: How can this problem be done if r isn't given?)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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**Topic: Rotational Kinetic Energy**

**Problem:**
Calculate the rotational kinetic energy of a spinning (not rolling) bowling ball with a mass of 12 kg, a radius of 0.20 m, and a velocity of 5 m/s.

*Fun Fact: How can this problem be solved if the radius (r) isn't provided?*

**Key Formulas and Concepts:**

1. **Relationship Between Linear and Angular Velocity:**
- \( v = r\omega \)
- Where \( v \) is linear velocity, \( r \) is radius, and \( \omega \) is angular velocity.

2. **Moment of Inertia (I) for Various Shapes:**
- **Sphere:** \( I_{\text{sphere}} = \frac{2}{5} MR^2 \)
- **Cylinder:** \( I_{\text{cylinder}} = \frac{1}{2} MR^2 \)
- **Ring:** \( I_{\text{ring}} = MR^2 \)
- **Stick (through center):** \( I_{\text{stick thru center}} = \frac{1}{12} ML^2 \)
- **Stick (through end):** \( I_{\text{stick thru end}} = \frac{1}{3} ML^2 \)

These equations allow calculation of the rotational kinetic energy using appropriate moment of inertia for the object's shape. The bowling ball in this instance is modeled as a sphere.

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