Answer to Question #125876 in Mechanics | Relativity for T

Question

5. At a given time a shaft is rotating 50 rpm about a fixed axis, 20 s later it is rotating 1050 rpm. Solve its angular acceleration.

Answer 1

By definition, the angular acceleration is:

$$\varepsilon = \dfrac{\Delta \omega}{\Delta t}$$

where $\Delta \omega$ is angular velocity change during the time $\Delta t$.

The $\Delta \omega$ can be calculated as following (as far as one revolution corresponds to $2\pi$ radians):

$$\Delta \omega = (1050rpm - 50rpm)\cdot 2\pi = 2000\pi \space rad/m \approx 104.7\space rad/s$$

Thus, the angular acceleration will be:

$$\varepsilon = \dfrac{104.7\space rad/s}{20s} \approx 5.2 rad/s^2$$

Answer. 5.2 rad/s^2.