Angular acceleration of a beam?

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Calculating the time for a beam to fall involves understanding angular acceleration, which varies with the beam's angle. The torque equation, torque = moment of inertia * angular acceleration, incorporates the angle and distance from the pivot point to the center of mass. Additionally, the kinematic equation s = -1/2gt^2 + Vt + s can help, but changing acceleration complicates the analysis. An energy-based approach may simplify the problem by determining the required angular velocity at different angles to conserve total energy. Researching the 'inverted pendulum' concept can provide further insights into solving this problem effectively.
risecolt
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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.
 
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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.
 
Google something called the 'inverted pendulum' for some insight how to solve this.
 

Thread 'Mousetrap Car Energy efficiency'

For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...
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