### 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).

Answered: Image /qna-images/answer/93da1ebb-9edc-4fbb-a885-0e9b7e7b5cd3.jpg

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

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)...

See similar textbooks

Similar questions

A disc rotates at 90 rpm (revolutions per minute).What is the angular speed (in rad/s)?
A cooling fan is turned off when it is running at 950 rev/minrev/min . It turns 1500 revolutions before it comes to a stop. What was the fan's angular acceleration, assumed constant?
A soccer ball whose radius is 11 cm rolls a distance of 10 m in 3.50 s. What is the angular speed of the ball?
A bicycle with 24-inch diameter wheels is traveling at 17 mi/h. Find the angular speed of the wheels in rad/min. How many revolutions per minute do the wheels make? Round your answer to three decimal places.
A flywheel is rotating at an angular velocity of 8 rad/s. It slows down at a rate of 2 rad/s?. How many revolutions will the flywheel make before coming to a stop?
A guinea pig is running on the exercise wheel in its cage. Theguinea pig is running at 2 miles per hour on the inside surface of thewheel that spins around its center axel. If the diameter of the wheel is8 inches, what is the revolutions per minute (rpm) of the wheel?
A barbell spins around a pivot at its center (see figure). The barbell consists of two small balls, each with mass m = 620 grams, at the ends of a very low mass rod whose length is L = 22 cm. The barbell spins with angular speed = 50 radians/s. Calculate Krot: Krot = 152.32 X J m @ m
A ball of radius 0.200 m rolls with a constant linear speed of 2.47 m/s along a horizontal table. The ball rolls off the edge and falls a vertical distance of 2.20 m before hitting the floor. What is the angular displacement of the ball while the ball is in the air?
June started winding up her arm holding a baseball, moving it around her shoulder in a circle, to get ready to throw. June’s arm is 0.5 m long and moves at an angular velocity of 2 rad/s. How much time will 10 revolutions take? What is the velocity of the baseball when she let go of it?
Two bugs, Buzz and Crunchy, are siting on a spinning disk. Buzz is sitting halfway and Crunchy is sitting at the outer edge as shown. The radius of the disk is 1.2 m and the disk is rotating with an angular speed of 20 rpm. What is Crunchy's speed, in m/s? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. Buzz Crunchy
A 20 cm diameter circular saw blade spins at 3900 rpm. How fast would you have to push a straight hand saw to have the teeth move through the wood at the same rate as the circular saw teeth?
A grinding wheel 0.35 mm in diameter rotates at 2100 rpm .What is the acceleration of a point on the edge of the grinding wheel?