## Horizontal 3D Circular Motion of Mass on a Table JavaScript WebGL Model

<h2>Horizontal Circular Motion of Mass on a Table</h2>

<p>A particle with mass m is moving with constant speed v along a circular orbit (radius r ). The centripetal force $$F=\frac{mv^2}{r}$$ is provided by gravitation force from another mass $$M=\frac{F}{g}$$. A string is connected from mass m to the origin then connected to mass M . Because the force is always in the r direction, so the angular momentum $$\widehat{L} = m\widehat{r} \widehat{v}$$  is conserved. i.e. $$L=mr^2\omega$$  is a constant. For particle with mass m:</p>

<p> $$m \frac{d^2r}{dt^2}=m\frac{dv}{dt}=mv^2r−Mg=\frac{L^2}{mr^3}−Mg$$</p>

<p> $$\omega = Lmr^2$$ </p>

<h2>Controls</h2>

<p>You can change the hang mass M or the on the table mass m or the radius r with sliders. The mass M also changed to keep the mass m in circular motion when you change r. However, if you change mass M , the equilibrium condition will be broken. </p>

Horizontal Circular Motion of Mass on a Table

### Translations

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### Software Requirements

SoftwareRequirements

 Android iOS Windows MacOS with best with Chrome Chrome Chrome Chrome support full-screen? Yes. Chrome/Opera No. Firefox/ Samsung Internet Not yet Yes Yes cannot work on some mobile browser that don't understand JavaScript such as..... cannot work on Internet Explorer 9 and below

### Credits

Fu-Kwun Hwang - Dept. of Physics, National Taiwan Normal Univ. and lookang; lookang; tinatan

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http://iwant2study.org/lookangejss/02_newtonianmechanics_6circle/ejss_model_circular3dfr02wee/circular3dfr02wee_Simulation.xhtml

### Learning Content

Motion in a Circle Content taken from http://www.seab.gov.sg/content/syllabus/alevel/2017Syllabus/9749_2017.pdf

1. Kinematics of uniform circular motion
2. Centripetal acceleration
3. Centripetal force

### Learning Outcomes

Candidates should be able to:

1. express angular displacement in radians
2. show an understanding of and use the concept of angular velocity to solve problems
3. recall and use v = rω to solve problems
4. describe qualitatively motion in a curved path due to a perpendicular force, and understand the centripetal acceleration in the case of uniform motion in a circle
5. recall and use centripetal acceleration a = rω 2 , and $$a = \frac{v^2 }{r}$$ to solve problems
6. recall and use centripetal force F = mrω 2 , and $$F = \frac{mv^2}{r}$$ to solve problems.

For Teachers

A particle with mass $$m$$ is moving with constant speed $$v$$ along a circular orbit (radius $$r$$). The centripetal force $$F=m\frac{v^2}{r}$$ is provided by gravitation force from another mass $$M=F/g$$.
A string is connected from mass m to the origin then connected to mass $$M$$.
Because the force is always in the $$\hat{r}$$ direction, so the angular momentum $$\vec{L}=m\,\vec{r}\times \vec{v}$$ is conserved. i.e. $$L=mr^2\omega$$ is a constant.

For particle with mass m:

$$m \frac{d^2r}{dt^2}=m\frac{dv}{dt}= m \frac{v^2}{r}-Mg=\frac{L^2}{mr^3}- Mg$$
$$\omega=\frac{L}{mr^2}$$

The following is a simulation of the above model.

When mass m or radius r is changed with sliders, equilibrium condition is recalulated for constant circular motion.
However, if mass M is changed, the equilibrium condition will be broken, and the system will oscilliate up and down.

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### Video

Ejs Open Source Horizontal Circular Motion java applet by lookang lawrence wee

### Version:

1. http://weelookang.blogspot.sg/2016/03/horizontal-3d-webgl-circular-motion-of.html HTML5 JavaScript WebGL version by Loo Kang Wee and Tina Tan
2. http://weelookang.blogspot.sg/2010/07/lesson-on-circular-motion-with-acjc.html 09 July 2010 Computer Lab hands on learning session on  Ejs Open Source Vertical Circular Motion of mass m attached to a rod java applet side view of the same 3D view with teacher explaining the physical setup of the mass m and mass M attached by a string through a table with a fricitionless hole in the middle of table for string to go through and student working on their own desktop
3. http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1883.0 remixed Java applet by Loo Kang Wee
4. http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1454.0 original Java applet by Fu-Kwun Hwang

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