The Mystery Behind the Fan's Circular Motion

AI Thread Summary
When a finger is placed in the center of a fan, it experiences a larger circular motion due to the movement of the fan blades around it. The center of the fan is a fixed point, while the blades are in motion, creating a larger radius for the finger's tip. Friction can cause the finger to shift slightly from the exact center, contributing to the circular motion observed. Pressing the finger firmly against the center minimizes movement, demonstrating the relationship between the fan's rotation and the position of the finger. Understanding this concept highlights the dynamics of rotational motion in fans.
unique_pavadrin
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Homework Statement


Hey just a quick question that bothering me:

how come when u stick your finger in the middle of the fan and let it move it goes in a larger circle?
 
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Only the centre of the fan is not moving. But that's a one dimensional point. All other points on the fan are moving. The tip of your finger is a 2-d surface. Generally, due to friction, your finger will get shifted ever so slightly from the exact centre, and so you'll see it going around in a circle.

If you press it hard against the centre, you'll see it doesn't move much. But don't try it.
 
okay thanks makes sence
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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