Circulation Motion and Centrifugal 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.

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

`AuthorˇGFu-Kwun Hwang, Dept. of physics, National Taiwan Normal University`
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