why does rotating a ball on a string faster makes it horizontal

musik132

Hi suppose i had a ball on string and started to rotate it in a circle around my hand. When i increase the speed of the ball it becomes more and more horizontal.
The only forces i can think of at play is centripetal and centrifugal forces and the force exerted by my hand and gravity. Is somehow the centripetal force's verticle component greater than the centrifugal's or is it something else?

Simon Bridge

Actually - as you are looking at it, there is no centrifugal force.
There is the tension in the string which has radial and vertical components, and gravity, which is only vertical.

The vertical component of the tension has to be equal to gravity.
The horizontal component has to be the centripetal force.
The centripetal force is related to the angular velocity of the ball ... so what is happening is that to go faster the ball need more centripetal force - but only the same lift against gravity to hold it up. Since both these forces come from the same place (the tension in the string) then the string gets more horizontal.

It can never get completely horizontal though.


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From the POV of an ant-physicist on the ball, there is a gravity force pointing down and a centrifugal force pointing horizontally to it. There is also a tension force in the string which exactly balances the other two. The the string were at 45deg then the centrifugal force would be equal to the gravity force ... the faster the ball goes, the bigger the centrifugal force and so the bigger the horizontal component of the tension has to be to balance it.... so the angle has to be less than 45deg.

musik132

so just to check my thinking:
Ft = tension Fg = gravity Fc = centripetal
Ftcosθ = Fg and Fc=mrω^2=Ftsinθ
If ω increases the angle must go up but if the angle goes up doesnt Ftcosθ become less which would mean an increase in tension in order to counteract gravity? So an increase in ω changes both Ft and sinθ

and why isnt there a centrifugal force?
there is a "apparent outward force that draws a rotating body away from the center of rotation. It is caused by the inertia of the body as the body's path is continually redirected" wikipedia

CWatters

Indeed. To reach 90 degrees ω and the tension would need to be infinite.

Simon Bridge

That's exactly it - it is only an apparent force. The reference you used also explains.

It did not belong in your initial description because "you" doing the observing are not rotating with the ball. No reason for you to have an inertial correction. You do feel the ball pull back on the string but recall - you are providing the applied force to the center. This is an unbalanced force resulting in acceleration towards the center which you see as circular motion.

The ant in my description has a different POV. He sees no centripetal forces, but it does make sense to talk about his experience in terms of the centrifugal pseudoforce.

In Newtonian physics, the appearance of a pseudoforce in your physics is a clue that you are in an accelerating reference frame.