Question

An electric fan has blades of length 60 cm as measured from the axis of rotation. If the fan is rotating at 1200 rpm, the acceleration of a point on the tip of the blade is about:

a.4800 m /s2
b. 9600 m/s2
c. 3600 m/s2
d. 5000 m/s2​

Answer 1

Given:

An electric fan has blades of length 60 cm as measured from the axis of rotation.

To find:

If the fan is rotating at 1200 rpm, the acceleration of a point on the tip of the blade is about ?

Calculation:

First of all, we need to convert the unit of angular velocity from rpm to rad/sec:

$\therefore \: 1200 \: rpm = 1200 \times \dfrac{2\pi}{60} = 40\pi \: rad/s$

Now , we know that acceleration of the tip of the blade is actually the centripetal acceleration directed radially inwards :

$\therefore \: a_{c} = \dfrac{ {v}^{2} }{r}$

$\implies\: a_{c} = \dfrac{ {v}^{2} }{ {r}^{2} } \times r$

$\implies\: a_{c} = { (\dfrac{v}{r} )}^{2} \times r$

$\implies\: a_{c} = { \omega}^{2} \times r$

$\implies\: a_{c} = {(40\pi)}^{2} \times \dfrac{60}{100}$

$\implies\: a_{c} = 960 \times {\pi}^{2}$

Considering π² $\approx$ 10 :

$\implies\: a_{c} = 960 \times 10$

$\implies\: a_{c} = 9600 \: m/ {s}^{2}$

So, acceleration of tip of blade is 9600 m/s².