# Angular acceleration of a beam?

1. Mar 23, 2013

### risecolt

This problem is making me want to tear my hair off.
I am trying to calculate the time it takes for a beam to fall to the ground.

http://myweb.lmu.edu/gvarieschi/chimney/Graph1.JPG

It would be great if I could calculate the rate of change of angular acceleration, as the acceleration would depend on the angle.

The equation for momentum or torque = moment of inertia * angular acceleration = cos(angle) * arm * m*g

Here the arm would be equal to the distance from the point of rotation to the center of the mass of the beam.

The other equation I find useful is: s = -1/2gt^2 + Vt + s

Again, with changing acceleration, I am lost.

2. Mar 23, 2013

### jbriggs444

Consider an analysis based on energy. How fast must the bar be rotating as it passes through a given angle in order for total energy to be conserved?

That should then allow you to derive angular velocity as a function of angle.

That should lead you to a solution that does not involve solving a differential equation.

3. Mar 23, 2013

### Ryoko

Google something called the 'inverted pendulum' for some insight how to solve this.