Question

The force F⃗ pulling the string is constant; therefore the magnitude of the angular acceleration α of the wheel is constant for this configuration. Find the magnitude of the angular velocity ω of the wheel when the string has been pulled a distance d. Note that there are two ways to find an expression for ω; these expressions look very different but are equivalent.

Answer 1

Answer:

The answer is "$\boxed{\boxed{\omega = \sqrt{\frac{2fd}{kmr^2}}}}$"

Explanation:

$\to d= r \theta \\\\ \to \theta =\frac{d}{r}\\\\\to \omega^{r} - \omega_{0}^{r} = 2 \alpha \theta\\\\\to \omega^{r} = 2 \alpha \theta - \omega_{0}^{r} \\\\\to \omega^{r} = 2 (\frac{F}{Kmr}) \frac{d}{r}\\\\\to \omega = \sqrt{\frac{2fd}{kmr^2}}$