Question

An electric fan has blades of length $30 \,cm$ measured from the axis of rotation. If the fan is rotating at $120 \,rpm$, the acceleration of a point on the tip of the blade is

• A. $1600 \,ms^{-2}$
• B. $47.4 \,ms^{-2}$
• C. $23.7 \,ms^{-2}$
• D. $50.55 \,ms^{-2}$

Answer 1

Answer: (B)

Frequency of rotation $v=120\, rpm =2\, rps$
length of blade $r=30 \, cm =0.3\, m$
Centripetal acceleration $a=\omega^{2} r=(2 \pi v)^{2} r$
$=4 \pi^{2} v^{2} r=4 \pi^{2}(2)^{2}(0.3)=47.4 \, ms ^{-2}$