WOLFRAM|DEMONSTRATIONS PROJECT

Conic Pendulum

angular velocity

time

Lighter

:Darker[ColorData[97][2],0.7] should be a valid color directive, an image, or a list of them.

Lighter

:Darker[ColorData[97][1],0.58] should be a valid color directive, an image, or a list of them.

Lighter

:Darker[ColorData[97][3],0.75] should be a valid color directive, an image, or a list of them.

General

:Further output of Lighter::arg will be suppressed during this calculation.

MapThread

:Object ColorData[97,ColorList]〚{2,1,3,4,5,6,7,8,9,10}〛 at position {2, 2} in MapThread[{Specularity[White,#1],#2,Lighting#3}&,{{3,3,3,6,6,6,6,3,6,6},1,{{{Ambient,Lighter[Darker[ColorData[1][1],0.7],0.05]},{Directional,Darker[ColorData[97][2],0.7],ImageScaled[{0,2,2}]},{1},{Directional,Darker[ColorData[97][2],0.7],ImageScaled[{2,0,2}]}},9}}] has only 0 of required 1 dimensions.

The conic pendulum is a system consisting of a mass

hanging from a fixed point by a rope of length

. It spins around the vertical with angle

and with angular velocity

. As the angular velocity increases, the angle

from the vertical increases.

The forces acting on the mass are the weight

(red) and the tension

(green), with resultant the centripetal force

(magenta) equal to

Lsin(α)

. The velocity vector

is shown in yellow.

Finally, the relation between the angular velocity and the angle is

tan(α)=

For simplicity, the mass is taken as 1 kg and the radius equal to 1 m.