Question 2.SP.26: In Problem 2.25, how many revolutions does the flywheel make......
In Problem 2.25, how many revolutions does the flywheel make in attaining its speed of 2000 rpm?
To determine the number of revolutions \theta, select the equation expressing the relation between \theta and the three given quantities \omega_{0}, \omega, t. Of course, a formula may be used involving the angular acceleration \alpha just determined, but it is advisable to proceed with data given in the problem to derive the value \theta independently of \alpha, which could by chance have been found incorrectly:
\theta=\frac{1}{2}\left(\omega+\omega_{0}\right) t=\frac{1}{2}(209+0)(20)=2090 \mathrm{rad}
To express \theta in revolutions,
\theta=\frac{2090 \mathrm{rad}}{2 \pi \mathrm{rad} / \mathrm{rev}}=\underline{333 \mathrm{rev}}
The same result is obtained using \omega \text{ in } \mathrm{rev} / \mathrm{s} as follows:
\theta=\frac{(2000 / 60) \mathrm{rev} / \mathrm{s} + 0 \mathrm{rev} / \mathrm{s}}{2} \times 20 \mathrm{~s}=\underline{333 \mathrm{rev}}