Try the fastest way to create flashcards
Question

# The angular velocity of a rotating rigid body increases from 500 to 1500 rev/min in 120 s. (a) What is the angular acceleration of the body? (b) Through what angle does it turn in this 120 s?

Solution

Verified
Step 1
1 of 3

a) From $\textbf{the kinematics of the rotational motion }$ we know that :

$\dfrac{1 \mathrm{rev}}{\mathrm{min}} \cdot \dfrac{2 \pi\; \mathrm{rad}}{\mathrm{rev}} \cdot \dfrac{1 \mathrm{min}}{60\ \mathrm{ s}}= 0.10479\ \;\mathrm{ rad/s}$

$\textbf{For}$ $\omega_{i} = 500$ rev/min :

$\dfrac{500 \mathrm{rev}}{\mathrm{min}} \cdot \dfrac{2 \pi\; \mathrm{rad}}{\mathrm{rev}} \cdot \dfrac{1 \mathrm{min}}{60\ \mathrm{ s}}= 52.3598\ \;\mathrm{ rad/s}$

$\textbf{For}$ $\omega_{f} = 1500$ rev/min

$\dfrac{1500 \mathrm{rev}}{\mathrm{min}} \cdot \dfrac{2 \pi\; \mathrm{rad}}{\mathrm{rev}} \cdot \dfrac{1 \mathrm{min}}{60\ \mathrm{ s}}= 157.079\ \;\mathrm{ rad/s}$

From the equation of the angular velocity we know that :

$\omega_{f} = \omega_{i} + \alpha t$

where:

• $\omega_{f}$ is the final angular velocity of the body.
• $\omega_{i}$ is the initial angular velocity of the body.
• $\alpha$is the angular acceleration of the body.
• $\theta_{i}$ is the initial angular displacement .
• $\theta_{f}$ is the final angular displacement .
• $t$ is the time .

From $\textbf{givens}$ we know that :$t = 120$ s , $\omega_{i} = 52.3598$ rad/s and $\omega_{f} = 157.079$ rad/s .

$\textbf{Entering }$ known information into :

\begin{align*} \omega_{f}& = \omega_{i} + \alpha t \\ \alpha t&= \omega_{f} - \omega_{i}\\ \alpha &= \dfrac{\omega_{f} - \omega_{i} }{t}\\ &= \dfrac{157.079 - 52.3598}{120}\\ &= 0.87266 \end{align*}

$\boxed{\alpha = 0.87266\ \; \mathrm{rad/s^2}}$

## Recommended textbook solutions #### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (8 more)Randall D. Knight
3,508 solutions #### Mathematical Methods in the Physical Sciences

3rd EditionISBN: 9780471198260 (1 more)Mary L. Boas
3,355 solutions #### Fundamentals of Physics

10th EditionISBN: 9781118230718 (3 more)David Halliday, Jearl Walker, Robert Resnick
8,971 solutions #### University Physics, Volume 1

1st EditionISBN: 9781938168277Jeff Sanny, Samuel J Ling, William Moebbs
1,471 solutions