Circulation Motion and Centripetal Force

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A red ball is attached to a green cord (neglect its mass)
passing through a small hole in a friction less, horizontal table.
The red ball is initially orbiting in a circle of radius r with velocity v.
A black ball is tied to the other end of the green cord.

If it is in equilibrium,

the gravitational force of the black ball Fg = Mg ,
provides the centripetal force Fc needed.

Fc = m v²/r = m w² r ( v=w*r )

Fg = Fc    i.e.  Mg = m w² r

1. Click the black ball and drag it up and down to change the radius r.

Click with left mouse button:
    The size (mass) of black ball will change to keep the system in equilibrium.
Click with right mouse button:
    The mass of black is the same. The system starts oscillation.

The angular momentum of the red ball is a constant of the motion.
L = r m v = m r² w = constant

When the radius r is changing,
    centripetal force Fc = (rmv)²/(mr³)= L²/(mr³) changes ,too.

    If you click the right mouse button and drag it up/down/left/right,
        you can rotate the coordinate system.

4. Click trace check box to trace the trajectory,
    Press Clean Button to clear the trace.

5. Parameters :
    A short white arrow represents the velocity vector v = r w.
    w : angular frequency
    r : radius
    Mg/m: Mg gravitation force for black ball,
       m is the mass of red ball.

Your suggestions are highly appreciated! Please click hwang@phy03.phy.ntnu.edu.tw

Author¡GFu-Kwun Hwang, Dept. of physics, National Taiwan Normal University

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