Rotating turntable simulation

Sean Wilson (s0091720@sms.ed.ac.uk), the School of Physics at the University of Edinburgh.

Introduction

The applet is a real time simulation of a rotatable turntable that allows you to investigate rotational dynamics. The animated diagram shows an overhead view of the turntable, with a red point mass and a blue massless fan on top of it, which represents a closed system which can be manipulated by the user.

Screenshot
Screenshot

Underlying Physics

In this simulation, air resistance is considered negligible and is ignored. The fan and the point mass can be moved along the radius of the turntable, the simulation can be paused and the rotational energy of the system can be reduced to zero using the controls.

The moment of intertia of the system varies according to the position of the point mass. The fan is massless so does not contribute to this. The fan exerts a force in the direction of the arrow, which can be varied in both magnitude and direction. This forces produces a variable torque on the turntable, causing it to rotate. The angular accleration of the turntable is then calculated using the moment of intertia of the system and the torque generated by the fan. The applet text pane shows all the calculations that are carried out to run the simulation. As the system state is updated in real time, it is useful to pause the simulation so that the results of calculations can be looked at.

Exercises

Some interesting behaviour can be observed under various conditions:

  1. Point the fan directly away or towards the turntable center. This will always produce no torque regardless of other factors.
  2. Point the fan exactly perpendicular to the direction of the turntable center. This will produce the most torque possible with the current fan position and force.
  3. Move the fan to the exact center of the turntable. This will always produce no torque regardless of other factors.
  4. Move the fan to the very edge of the turntable. This will produce the most torque possible with the current fan orientation and force.
  5. Try pointing the fan is various directions while it is applying a force. Notice the direction effects whether the system rotates clockwise or anticlockwise.
  6. When the turntable has angular momentum, move the point mass to the center of the turntable. This makes the system rotate fastest because the moment of intertia is smallest.
  7. When the turntable has angular momentum, move the point mass to the edge of the turntable. This makes the system rotate slowest because the moment of intertia is at its maximum.
  8. Move the fan to different positions while it is off and the turntable is turning. Notice that the linear velocity of the fan is highest when it is at the edge of the turntable and slowest closer to the center.
Requirements

To use the applet, you require a web browser which a Java plugin later than 1.2 (note it has not been tested with 1.2 - only 1.3.1 and 1.4), for example the latest JRE from Sun or Apple's JDK on Mac OS-X. You can also use the AppletViewer provided with your chosen JRE/JDK.

It is not recommended that you use a remote X-session to run this applet as it draws to the screen a lot and the resulting lag makes the animation jerky.

Installation

Unpack the applet - if it came with a group of other applets from the School of Physics at the University of Edinburgh, it should be in the turntable subdirectory. Inside the turntable directory should be some Java code, classes and a number of html files, including an index.html which should contain links to this documentation, JavaDoc for the simulator and an example of using the applet.

Usage

The provided html files give you an example configuration of the applet. "applet.html" shows a empy webpage containing the applet. You can set the size of this applet as usual. Below is an example html file which embeds a 640 pixels by 606 pixels version of the applet.

<html>
<head>
<title>Rotating turntable simulation</title>
</head>
<body>
<applet code="Turntable.class" width="640" height="606"></applet>
</body>
</html>


How the applet is used is up to the user - it could be used in lectures, embedded in online course material or any other use that could be conceived.

Known Bugs

There are no known bugs at present.

Additional Documentation

There is complete JavaDoc for the classes in this applet in the "javadoc" subdirectory of the applet directory.