Question

An electric fan has blades of length $30cm$ as measured from the axis of rotation. If the fan is rotating at $1200rpm$, the acceleration of a point on the tip of the blade is about

• A. 2370 $m{s}^{-2}$
• B. 5055 $m{s}^{-2}$
• C. 1000 $m{s}^{-2}$
• D. 4740 $m{s}^{-2}$

Answer 1

Answer: (D)

4740 $m{s}^{-2}$

$1$ rpm = $\frac{\pi }{30}$rad$s^{-1}$

so $\omega =1200\times \frac{\pi }{30}=40\pi$rad$s^{-1}$

acceleration of the point at the tip $={\omega }^{2}r=(40\pi {)}^2\times \frac{30}{100}=4737.41m{s}^{-2}$

and the closest answer is $4740m{s}^{-2}$.