Question

The tip of the blade of a fan rotates at 300 rpm. Find the average
speed of the tip (in metre per minute) if the blade length from the
centre is 3.5 m.​

Answer 1

Given:

Tip of fan rotates at 300 rpm.

Blade length is 3.5 m

To find:

Average speed of tip of fan blade (in m/min)

Calculation:

First , we will convert the angular velocity of the fan blade from rpm to radians per second.

$\therefore \: 300 \: rpm$

$= 300 \times \dfrac{2\pi}{60}$

$= 5 \times 2\pi$

$= 10\pi \: rad {s}^{ - 1}$

Linear velocity can be calculated from the product of angular velocity and the the length of the fan blade from the axis of rotation.

$v = r \times \omega$

$= > v = 3.5 \times 10\pi$

$= > v = 35\pi \: m {s}^{ - 1}$

Now , converting linear velocity from m/s to m/min:

$= > v = 35\pi \: m {s}^{ - 1}$

$= > v = 35\pi \: \dfrac{m}{s}$

$= > v = 35\pi \: \dfrac{m}{ (\frac{1}{60} \: min)}$

$= > v = 2100\pi \: \frac{m}{min}$

So , final answer is :

$\boxed{ \sf{ \bold{ v = 2100\pi \: \frac{m}{min} }}}$