I have need of a mathematical model of a mass at the end of a stick, pivoting about the opposite end. What I have done so far is not giving realistic results, would appreciate it if some one could point out my error.(adsbygoogle = window.adsbygoogle || []).push({});

Basic model :

[tex] \tau = I \ddot {\theta} [/tex]

[tex] I = m r^2 [/tex]

The system is being pushed by an air cylinder (force F) with the fixed end mounted a distance L directly below the pivot, the moving end of the cylinder is mounted a distance r along the pivot arm from the pivot point. With [itex] \phi [/itex] the angle between the cylinder and the pivot arm. So I have :

[tex] \tau = r F sin( \phi) [/tex]

My variable of interest will be the angle between the pivot arm and the line defined by the pivot and the fixed end of the cylinder, call this angle [itex] \theta [/itex]

By the law of sines I get

[tex] \frac {Sin(\phi)} {L} = \frac {sin(\theta)} {x} [/tex]

where x is the length of the cylinder.

I get x in terms of [itex] \theta [/itex] from the law of cosines

[tex] x^2 = L^2 + r^2 -2lr cos(\theta) [/tex]

The differential equation is:

[tex] \ddot{ \theta } = \frac { \tau } {I} [/tex]

See the attachment for a diagram.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Mass on a stick model.

**Physics Forums | Science Articles, Homework Help, Discussion**