3

So, I would like to know that sometimes I touch the fan while it is turned on and I can do it in the middle but can't on the edge of the fan because it hurts at the edges why?

Qmechanic
  • 220,844
Shivansh Maheshwari
  • 314

1 Answers1

6

When running laps on an elliptical running track as in the Olympic athelic disciplines, then imagine that you take the outermost path on the running track and that a friend of yours takes the innermost path. Your path is longer. Because it is farther from the centre. So, if you want to finish the race at the same time as your friend, then you will have to run faster.

This is the experience of each particle on the fan blades. They all must complete a full revolution during the same time period. Otherwise they separate from the blade, i.e. the blade would break apart.

But a particle farther out sweeps through a much longer circular path. Covering a longer distance in the same time requires the particle to move with a higher speed. When you stop the fan by touching the tip far from the rotational centre, then a much faster particle impacts your finger - absorbing this extra energy and momentum is what makes it hurt more.

Note that the particle at the very centre is ideally not moving at all, only rotating about itself. So you cannot say that a particle at the tip moves with double the speed of the one at the centre, but it does move double as fast as a particle halfway. Also note that there might be other factors involved when "measuring" pain, such as the fan blade shape.

Physically we can talk about this by referring to the rotational - also called angular - proporties of the particles. All particles must move with the same angular velocity $\omega$, meaning the same number of revolutions per minute (or same angle per time unit, to be precise). The (translational) velocity, which is distance per time unit, is then found using a so-called geometric bond, which applies for rigid objects:

$$v=r\omega,$$

where $r$ is the distance from the rotational centre to the particle we are looking at. With this you can always find the speed of a particle at any distance , if you can just measure the angular speed first.

Steeven
  • 53,191