Question

The blades of a ceiling fan start from rest and, after two revolutions, have an angular speed of 0.5 rev/s. The angular acceleration of the blades is constant. What is the angular speed after eight revolutions?

Answer 1

Answer:

$\omega_f = 1 rad/s$

Explanation:

Given,

After two revolutions, angular speed = 0.5 rev/s

Angular speed after 8 revolution = ?

Using equation of circular motion

$\omega_f^2 = \omega_0^2 + 2\alpha \theta$

$0.5^2 =0^2 + 2\times \alpha\times 2$

$\alpha = 0.0625 rad/s^2$

Now, Angular speed after 8 revolution

$\omega_f^2 = \omega_0^2 + 2\alpha \theta$

$\omega_f^2 =0^2 + 2\times 0.0625 \times 8$

$\omega_f = 1 rad/s$

Hence, the angular speed after 8 revolution is equal to 1 rad/s.