 #1
birulami
 155
 0
Consider a freely rotating body. Let the axis of rotation be the zaxis. For simplicity assume all the mass of the body is concentrated in the xyplane, i.e. the plane in which the body rotates.
I have read about the moment of inertia tensor on wikipedia, but I don't see how I would combine it with a torque to tilt the axis of rotation.
Suppose the above rotating body indeed has a solid axis, albeit of zero mass, sticking out at one end with length [itex]\gt l[/itex]. At [itex]z=l[/itex] we apply a force perpendicular to the axis for a distance of [itex]\Delta s[/itex] in the direction of [itex]x[/itex].
What will happen to the to the overall rotation.
a) Will the axis tilt only a certain amount or does the force applied induce a rotation that keeps going and combines with the previous rotation.
b) What is the formula to get the tilt angle or the angular speed? I assume it somehow combines the inertia tensor and the force F or torque [itex]l\times F[/itex]?
Thanks,
Harald.
I have read about the moment of inertia tensor on wikipedia, but I don't see how I would combine it with a torque to tilt the axis of rotation.
Suppose the above rotating body indeed has a solid axis, albeit of zero mass, sticking out at one end with length [itex]\gt l[/itex]. At [itex]z=l[/itex] we apply a force perpendicular to the axis for a distance of [itex]\Delta s[/itex] in the direction of [itex]x[/itex].
Code:
< apply force


===== < xy plane of rotation
What will happen to the to the overall rotation.
a) Will the axis tilt only a certain amount or does the force applied induce a rotation that keeps going and combines with the previous rotation.
b) What is the formula to get the tilt angle or the angular speed? I assume it somehow combines the inertia tensor and the force F or torque [itex]l\times F[/itex]?
Thanks,
Harald.