Question

A fan rotates at 100 rpm. Find its angular velocity and linear velocity if tip of the blades are 0.20 m away from the axis of rotation.

Answer 1

The fan rotates at 100 rpm. RPM stands for Revolutions Per Minute.

This means that the fan completes 100 revolutions in one minute. 

Now, one revolution consists of $360^{\circ}$ or $2\pi$ radians. 100 revolutions are covered in 60 seconds. So we can find the angular speed as follows:

$\omega = \frac{\text{Angle covered}}{\text{Time taken}} \\ \\ \\ \implies \omega = \frac{100 \times 2\pi \, \, rad}{60 \, \, s} \\ \\ \\ \implies \boxed{\omega=\frac{10\pi}{3} \, \, rad/sec} \\ \\ \\ \implies \boxed{\omega \approx 10.472 \, \, rad/sec}$


Thus, we have obtained the angular speed. Now we need the linear speed of  the tip. 


The tip is at a distance of 0.20 metres from the axis of rotation.

We can find the linear speed as follows:

$v = r\omega \\ \\ \\ \implies v = 0.20 \times \frac{10\pi}{3} \\ \\ \\ \implies \boxed{v=\frac{2\pi}{3} \, \, m/s} \\ \\ \\ \implies \boxed{v \approx 2.094 \, \, m/s}$

Thus, we have also obtained the angular speed as well as the linear speed of tip of fan. 


Hope it helps
Purva
Brainly Community