## Related questions with answers

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

VerifiedAnswered 7 months ago

Answered 7 months ago

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:

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

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