Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 13 - Exercises and Problems - Page 239: 53


a) The proof is below. b) $\vec{v}=\omega A cos(\omega t)\hat{i}+\omega Asin(\omega t)\hat{j}$ c) $\omega A$ d) $\omega$

Work Step by Step

a) We factor to find: $\vec{v}= A((cos\omega t)\hat{i}-sin(\omega t )\hat{j})$ We see that this is a circle, so we see that there is a constant distance of $A$. b) We take the derivative of position to find the velocity: $\vec{v}=\omega A cos(\omega t)\hat{i}+\omega Asin(\omega t)\hat{j}$ c) The magnitude of the velocity vector is equal to the value of what the whole vector is multiplied by, which is $\omega A$. d) We see that the object's angular speed is $\omega$ using the original equation.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.