Circulation Motion and Centripetal Force

[Fu-Kwun Hwang]

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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 r²
 w = 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.
  where w : angular frequency , r : radius
  Mg/m: Mg gravitation force for black ball, m is the mass of red ball.

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Subject: Physics applets comments
Date: Wed, 28 Apr 1999 12:56 -0500 (CDT)
From: Michael Blackstock <michael.blackstock@wcom.com>
To: hwang@phy03.phy.ntnu.edu.tw
Fu-Kwun Hwang,

  Hello, I am an amateur American physics enthusiasts. Your physics
page has caught my attention and I would like to let you know they
are wonderful.
  Under Dynamics on 6. Circulation motion and Centripetal force, I
would like to know if it possible to change the velocity of the circular
motion and change both the weights on either end of the string without
changing it's radius?
 

Thank you,

Michael Blackstock


--------------------------------------------------------------------------------

Subject: Re: Physics applets comments
Date: Fri, 30 Apr 1999 10:46 -0500 (CDT)
From: Michael Blackstock <michael.blackstock@wcom.com>
To: hwang@phy03.phy.ntnu.edu.tw
Fu-Kwun Hwang,

  Thank you very much for the adjustments you made to the following
request I sent you!

Sincerely,

Subject: http://www.phy.ntnu.edu.tw/java/circularMotion/circular3D_e.html
Date: Sat, 09 Oct 1999 12:15:20 -0400
From: A Friend <a.friend@oln.com>
To: hwang@phy03.phy.ntnu.edu.tw
nice page.

thank you.

[a_a_quintero]

awesome webpage.  thank you very much for these applets.  they are a great help in understanding the concepts.  once again, thank you very much

alex

[physicsbysabbs]

Hi, I think this applet is great and I want to use it for my high school physics class.

My goal is to have my students investigate the relationships involved in circular motion.

I want them to understand the relationship between the following
- the centripetal force as a function of mass (with velocity and radius remaining constant)
- the centripetal force as a function of velocity (with mass and radius remaining constant)
- the centripetal force as a function of radius (with velocity and mass remaining constant)

With the applet, I have successfully been able to accomplish the third, but I can not find a way to manipulate for the other two.

Is there a way that can be done?

Thank you,
Nicole

[Fu-Kwun Hwang]

The condition for the system in equilibrium is: Mg = m w2r =m v2/r .
The mass m is the same in the above simulation.

First right click to pause the simulation.
LEFT Click at the black dot (mass M) and drag it up and down, you will change r and M at the same time. (Keep the total length of the string the same).
There is no way to keep the system in equilibrium if you change radius r ,and keep velocity v and mass M remaining constant.

If you LEFT Click at the red dot (mass m) and drag the mouse, you will change velocity v and mass M at the same time. (keep r the same).

For your cases:
- the centripetal force as a function of mass M(with velocity v and radius r remaining constant)
Then m is proportional to M.
- the centripetal force as a function of velocity v(with mass M and radius r remaining constant)
Then m is proportional to v2
- the centripetal force as a function of radius r (with velocity v and mass M remaining constant)
Then m is proportional to 1/r

Do you really want to simulate the above situations?

[lookang]

Hi, I think this applet is great and I want to use it for my high school physics class.

My goal is to have my students investigate the relationships involved in circular motion.

I want them to understand the relationship between the following
- the centripetal force as a function of mass (with velocity and radius remaining constant)
- the centripetal force as a function of velocity (with mass and radius remaining constant)
- the centripetal force as a function of radius (with velocity and mass remaining constant)

With the applet, I have successfully been able to accomplish the third, but I can not find a way to manipulate for the other two.

Is there a way that can be done?

Thank you,
Nicole

Did this help??
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=817.msg3090#msg3090
follow the link and download the *.jar file for the applet

[Fu-Kwun Hwang]

Here is an EJS version of the same applet.

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