When an object is in circular motion, it need centripetal force.

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.
2. The torque acting on the red ball is zero since F is parallel to r.
The angular momentum of the red ball is a constant of the motion.
L = r m v = m r²w = constant

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

3. Click the right mouse button to pause, click it again to resume.
       When the animation is suspended, Click at the red ball and drag the mouse button to change its tangential vector, and the mass of black ball will also change to keep in the same radius. 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.