**Educational Exercise: Calculating Angular Speed****Required Information:**A soccer ball with a diameter of 28.0 cm rolls without slipping at a linear speed of 4.80 m/s.**Question:**What is the ball’s angular speed?**Answer:**To find the angular speed (\(\omega\)) of the ball, use the relationship between linear speed (\(v\)) and angular speed:\[v = \omega \times r\]where \(r\) is the radius of the ball.First, convert diameter to radius:- Diameter = 28.0 cm- Radius (\(r\)) = 28.0 cm / 2 = 14.0 cm = 0.14 mNow, solve for angular speed:\[\omega = \frac{v}{r} = \frac{4.80 \, \text{m/s}}{0.14 \, \text{m}} = 34.29 \, \text{rad/s}\]Thus, the ball's angular speed is approximately 34.29 rad/s.

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Answered: Required information A soccer ball of…

Science

Physics

Required information A soccer ball of diameter 28.0 cm rolls without slipping at a linear speed of 4.80 m/s.

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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Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

**Educational Exercise: Calculating Angular Speed**

**Required Information:**
A soccer ball with a diameter of 28.0 cm rolls without slipping at a linear speed of 4.80 m/s.

**Question:**
What is the ball’s angular speed?

**Answer:**
To find the angular speed (\(\omega\)) of the ball, use the relationship between linear speed (\(v\)) and angular speed:
\[
v = \omega \times r
\]
where \(r\) is the radius of the ball.

First, convert diameter to radius:
- Diameter = 28.0 cm
- Radius (\(r\)) = 28.0 cm / 2 = 14.0 cm = 0.14 m

Now, solve for angular speed:
\[
\omega = \frac{v}{r} = \frac{4.80 \, \text{m/s}}{0.14 \, \text{m}} = 34.29 \, \text{rad/s}
\]

Thus, the ball's angular speed is approximately 34.29 rad/s.

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