Answer to Question #101785 in Mechanics | Relativity for kwikiriza steven

Question

angular velocity of a fan increases from
1
20 
rad s
to
1
30 
rad s
in 5s. Find the angular

acceleration and the total angle

Answer 1

If the fan accelerates from 20 rad/s to 30 rad/s in 5 seconds, its angular acceleration can be found as follows:

$$\alpha=\frac{\Delta\phi}{\Delta t}=\frac{\omega_2-\omega_1}{\Delta t}=\frac{30-20}{5}=2\text{ rad/s}^2.$$

The total angle:

$$\phi=\frac{\alpha t^2}{2}=\frac{2\cdot 5^2}{2}=25\text{ rad}.$$