Physics of a Table Fan
By Abbey Bonino
Over Thanksgiving break I was able to get together with my extended family, which included my wonderful, but naive, younger cousin. As we were all congregated in a small space, my mother had set out a couple table fans to circulate the air more effectively. Unfortunately, this prompted my cousin to almost stick his finger in the fan, claiming that because he “couldn’t see each of the blades anymore, they must not be there to hurt me.” I quickly explained to him that this was not true, and that putting your hand in the way of the blades could really hurt it!
As I thought about my explanation to get him to stop, it made me curious just how fast these fan blades were spinning – I could now apply my new knowledge of angular quantities to make sense of this situation! I found the box of the fan in our basement, which stated on the back that the revolutions per minute (rpm) of the blades on the “high” setting is 1,450 rpm. Converting this to revolutions per second (rps), this value is equivalent to 24.2 rps, or 24.2 Hz, which is the frequency (f). Taking the reciprocal of this value (1/24.2 rps) gives the period (T), being 0.0414 seconds per revolution. Then, as the angular velocity (ω) is equal to 2π/T, I calculated ω to be 151.8 radians per second. To make this value easier to conceptualize, I converted the angular velocity to linear velocity using the formula v = r ω. I measured the radius (r) of the fan to be 30.5 cm, which is 0.305 meters. This value allowed me to calculate the linear velocity, which comes out to be 46.3 m/s. This value is equivalent to 103.6 mph - the blades are spinning extremely fast, fast enough to harm you if you impede their movement with your hand!
Calculations:
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