### Calculating Angular Speed of a Roller**Problem Statement:**A printing press has a roller 17 inches in diameter. A point on the roller's surface moves at a speed of 85 feet per second. What is the roller's angular speed?**Step-by-Step Solution:**1. **Convert Diameter to Radius:** - Diameter of the roller \( D = 17 \) inches - Radius \( r = \frac{D}{2} = \frac{17}{2} = 8.5 \) inches2. **Convert Radius to Feet:** - Since 1 foot = 12 inches, then: \[ r = \frac{8.5}{12} \text{ feet} \approx 0.7083 \text{ feet} \]3. **Determine Linear Speed:** - Linear speed \( v = 85 \) feet per second4. **Use the Angular Speed Formula:** - Angular speed \( \omega \) is given by: \[ \omega = \frac{v}{r} \] - Plugging in the values: \[ \omega = \frac{85 \text{ feet/second}}{0.7083 \text{ feet}} \approx 120 \text{ radians/second} \]5. **Round Answer:** - Angular speed to the nearest hundredth: \[ \omega \approx 120.00 \text{ radians/second} \]**Result:**The roller's angular speed is \( \boxed{120.00} \) radians per second (rounded to the nearest hundredth).

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Answered: A printing press has a roller 17 inches…

A printing press has a roller 17 inches in diameter. A point on the roller's surface moves at a speed of 85 feet per second. What is the roller's angular speed?

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter7: Rotational Motion And The Law Of Gravity

Section: Chapter Questions

Problem 69AP: A piece of mud is initially at point A on the rim of a bicycle wheel of radius R rotating clockwise...

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