Kinematics of Inverted Physical Pendulum

[HoloBarre]

Homework Statement

A stick of mass M, length L, stands upright on a table, pivoted to the table.

What is the angular velocity as it hits the table?

Homework Equations

ang. accel = (3g/2L)cos theta

w = (3g/2L) integral cos theta dt

The Attempt at a Solution

theta (t) = ?

Solution involves elliptic integrals?? Not familiar with numeric methods.

Any approximation of the velocity at the table would be good for now.

 

[aim1732]

Why don't you conserve mechanical energy?

 

[AtticusFinch]

Why don't you conserve mechanical energy?

Yeah this seems right. All you need to use is the parallel axis theorem, find the initial potential energy and solve for omega noting that the stick gains both rotational and translational kinetic energy.

 

[aim1732]

Translational?

 

[AtticusFinch]

linear kinetic energy 1/2mv² instead of 1/2Iw²

Actually thinking about it, it's not rolling so there probably wouldn't be translational kinetic energy gained.