Circulation Motion and Centripetal Force

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 frictionless, 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 gravitationa 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 r² w = constant

  When the radius r is changing,

  • centripetal force Fc= (rmv)²/(mr³)= L²/(mr³) changes ,too.

3. Click the mouse button to pause, click it again to resume.

4. Click trace checkbox to trace the trajectory,

• Press Clean Button to clear the trace.

5. Parameters :

• A short white line 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.

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