I throw a metal rod (not light) into the air

[jewbinson]

It is cylindrical in shape and is solid (not hollow) and has uniform density. Igonre air resistance.

It spins with some angular velocity omega and spins in the other possible ways.

Apart from omega, how many more degrees of freedom is possible?

I can find the MOI of a rod spinning with just angular velocity omega on a horizontal table, and hence the Lagrangian (and Hamiltonian).

But what about with these extra DOF?

I'm not familiar with working out the MOI for more than 1 DOF.

Thanks for your help in advance.

 

[phinds]

there are 3 total --- roll, pitch, and yaw

 

[jewbinson]

Ok... do we treat the motion of the rod as a whole (projectile motion) seperately or is that included in our calculation? Can someone please point me in the right direction of where to start? I have no clue...

 

[phinds]

The center of mass of the rod doesn't care about the rest of the motion, it travels in a parabola. This is a bit simplistic, probably, since if the cylinder is rotating at a high speed I'm not sure what the effect of that is, but there may be one ... I don't remember the physics of it.

 

[jewbinson]

Sounds like it might be a magnetic effect you're thinking of... if not then I would be interested as to what the effect you are thinking of is.

 

[phinds]

Sounds like it might be a magnetic effect you're thinking of... if not then I would be interested as to what the effect you are thinking of is.

No, not magnetic, it's an effect due to rotational inertia. I think it may not appy here since I seem to recall that it only has an effect when a roating cylinder is subjected to a an off-center force. The classical physics class experiment that demonstrates what I'm talking about is where you hold the free-spinning axle of a bicycle tire and have someone rev it up quite a bit and then you try to move one side of the axle towards you and the other away from you. It doesn't go in the direction you expect, it moves differently. Might be called precession. It's been about 50 years since I saw the experiment and I don't do physics.

EDIT: Might be the effect happens not from an off-center force so much as any force that tries to change the direction of the axis of rotation.

 

[jewbinson]

I think I might have come across what you describe.

If you spin an empty bottle of water in suspended air ("roll"), the angular velocity decreases with time

 

[m.e.t.a.]

It spins with some angular velocity omega and spins in the other possible ways.

Apart from omega, how many more degrees of freedom is possible?

there are 3 total --- roll, pitch, and yaw

For an object in freefall, I would think that the number of degrees of rotational freedom is 1. I.e., it doesn't matter what the object's angular velocity is about the x, y and z axes—these perpendicular angular velocities always resolve into a single angular velocity about a single axis of rotation. (I could be wrong, however...)