Try Magic Notes and save time.Try it free
Try Magic Notes and save timeCrush your year with the magic of personalized studying.Try it free
Question

# When the string is pulled with a force $p$ tangent to the rim, it gives the cylinder an angular acceleration $\alpha$, if the cylinder had fourfold the radius but everything else was the same the angular acceleration would be?

Solution

Verified
Step 1
1 of 2

### Explanation:

As we know, the angular acceleration of the cylinder is equal:

$\alpha=\dfrac{\tau}{I}$

Where $\tau$ is the torque, and $I$ is the moment of inertia. For the cylinder, the previous equation will be:

\begin{aligned} \alpha_1&=\dfrac{2 \tau}{mR^2} \tag{1} \end{aligned}

Rearrange the last equation. For the situation when $R=4R$, which is the case in our problem:

\begin{aligned} \alpha_2&=\dfrac{2 \tau}{m (4R)^2}\\ \alpha_2&=\dfrac{2 \tau}{16mR^2} \end{aligned}

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

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

3rd EditionISBN: 9780471198260Mary L. Boas
3,355 solutions #### Introduction to Quantum Mechanics

3rd EditionISBN: 9781107189638 (2 more)Darrell F. Schroeter, David J. Griffiths
485 solutions #### Fundamentals of Physics

10th EditionISBN: 9781118230718David Halliday, Jearl Walker, Robert Resnick
8,971 solutions