Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 10 - Rotation - Problems - Page 287: 6d

Answer

$6\dfrac {rad}{s^{2}}$

Work Step by Step

To find the angular acceleration, we need to find the angular velocity first. So, the angular velocity of point is: $w\left( t\right) =\dfrac {\partial \left( \theta \right) }{\partial t}=\dfrac {\partial }{\partial t}\left( 4t-3t^{2}+t^{3}\right) =4+3t^{2}-6t...................(1)$ The angular acceleration at any given time is: $\alpha \left( t\right) =\dfrac {\partial w}{\partial t}=\dfrac {\partial }{\partial t}\left( 4-6t+3t ^{2}\right)=6t-6 ............................(2)$ So using (2) and $t=2s$, we get: $\alpha \left( 2\right) =6\times 2-6=6\dfrac {rad}{s^{2}}$
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