# Simulations

## Template for Creating GeoGebra Animations

In an introductory sharing for the use of GeoGebra to my colleagues, I have prepared a simple template for them to try their hands at animations of points and other elements.

You can try the same too. Create a moving point by typing into the Input field (5,5*sin(time)) so that you get a point at x = 5 that oscillates between 5 and -5 in the vertical direction.

## Relationship between displacement-time and velocity-time graphs

Through this GeoGebra app, students can observe how the gradient of the displacement-time graph gives the instantaneous velocity and how the area under the velocity-time graph gives the change in displacement.

In the GeoGebra app below, you will see a displacement-time graph on the left and its corresponding velocity-time graph on the right. These graphs will be referring to the same motion occuring in a straight line. Instructions

1. Click “Play” and observe the values of displacement and velocity change in each graph over time.
2. Note the relationship between the gradient in the displacement-time graph and the value of velocity.
3. Note the relationship between the area under the velocity-time graph and the value of displacement.

## Instantaneous vs Average Velocity

This GeoGebra app allows students to observe the difference between instantaneous and average velocity from a graphical perspective.

## Uniform vertical circular motion

The following GeoGebra app simulates the force vectors on an object in uniform vertical circular motion.

A real world example of this would be the forces acting on a cabin in a ferris wheel.

<iframe scrolling="no" title="Vertical Uniform Circular Motion " src="https://www.geogebra.org/material/iframe/id/t5jstqsm/width/640/height/480/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/true/rc/false/ld/false/sdz/false/ctl/false" width="640px" height="480px" style="border:0px;"> </iframe>

## Vertical Non-Uniform Circular Motion

This is a simulation that shows the vectors of forces acting on an object rolling in a vertical loop, assuming negligible friction.

To complete the loop, the initial velocity must be sufficiently high so that contact between the object and the track is maintained. When the contact force between the object and its looping track no longer exists, the object will drop from the loop.

The following code is for embedding in SLS.

<iframe scrolling="no" title="Vertical non-uniform circular motion" src="https://www.geogebra.org/material/iframe/id/ny3jhhsp/width/640/height/480/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/true/rc/false/ld/false/sdz/false/ctl/false" width="640px" height="480px" style="border:0px;"> </iframe>

## Aircraft Turning in a Circle: a 3-D Visualisation with GeoGebra

This GeoGebra app is a 3-D visualisation tool of the force vectors acting on an aircraft turning with uniform circular motion in a horizontal plane.

I prepared this in advance as I will be lecturing on this JC1 topic next year.