Answer to Question #88464 in Mechanics | Relativity for Emmanuel

Question

The wheel, rotating at uniformly accelerated speed, after a time t =1min after the start of rotation, acquires a frequency on n=720rmp. Find the angular acceleration e of the wheel and number of revolutions N of the wheel during this time

Answer 1

The angular velocity

$$\omega=\omega_0+\varepsilon t$$

So, frequency

$$2\pi n=2\pi n_0+\varepsilon t$$

Finally, the angular acceleration

$$\varepsilon=\frac{2\pi n_0}{t}=\frac{2\pi \times\frac{720\:\rm{rev}}{60\:\rm{s}}}{60\:\rm{s}}=0.4\pi\:\rm{s^{-2}}=1.256\:\rm{s^{-2}}$$

The number of revolutions

$$N=\frac{\frac{\varepsilon t^2}{2}}{2\pi}=\frac{0.4\times 60^2}{4}=360\:\rm{rev}$$