- #1

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## Homework Statement

I am trying to understand where the forces in the inverted pendulum comes from starting with this horizontal force equation:

http://www.engin.umich.edu/group/ctm/examples/pend/inveq2.GIF

It is associated with this picture http://www.engin.umich.edu/group/ctm/examples/pend/invFBD.GIF

from this website

The variables are:

m = mass of pendulum

l = length to pendulum center of mass

θ = angle

[itex]\dot{θ}[/itex] = angular velocity

[itex]\ddot{θ}[/itex] = angular acceleration

## Homework Equations

http://www.engin.umich.edu/group/ctm/examples/pend/inveq2.GIF

I understand the first term is the transitional motion, but I don't know why there are two rotational motion terms, which looks the same but are different in the diagram, looks like it is 90 degrees apart. I understand why the 2 terms on the left are opposite of each other in sign, but i don't know why one uses [itex]\ddot{θ}[/itex] while the other uses [itex]\dot{θ}[/itex][itex]^{2}[/itex]

## The Attempt at a Solution

I first thought this had to do with parallel axis theorem, but this equation is calculating the sum of horizontal forces, not inertia. In the end, the two term breaks down to ([itex]\frac{dθ}{dt}[/itex])[itex]^{2}[/itex] and [itex]\frac{d^{2}θ}{dt^{2}}[/itex]. What is the difference, if any between these two? i know one is angular velocity squared and the other one is angular acceleration, but i don't know where that angular velocity comes from.

thanks for all the answers!