I can imagine a pencil rotating about an axis parallel to its length and perpendicular to its length at the same time and I have also seen several self balancing mechanisms online (got no idea wt that is) where a ball spins in multiple directions
So what do they mean by an object can only have one axis of rotation?
In: Physics
If an object is rotating one way, and you try to rotate it another, the two just add together to create the final direction.
It’s like how an object can’t move in two directions at once. Any two directions add up to a new single direction. North and west just becomes northwest.
There is a place I need to be standing. It is located 4 steps to the east, and 3 steps north. I walk 5 steps in a diagonal northeast and arrive at my destination. I didn’t travel north or east; I traveled northeast. Ignoring cardinal directions, this is true for any line in 2 dimensions, we can split our direction vector into its components, but that doesn’t change the direction we went. The same is true in 3D (and in fact we can still use the Pythagorean theorem)! If we wish to travel 3 steps north, 4 steps east, and 5 steps directly up, We can travel about 7 steps to arrive at our destination in space.
any way you try to do a constant rotation an object around 2 axis, there is always 1 other axis were rotating around that axis looks exactly the same. so that is the axis of rotation.
its like saying “you can only walk in a streight line in 1 direction”, you might say “but I am walking north AND east, thats 2 directions” to which I respond “no, thats 1 direction north-east”
Hey, I’ve had the same conceptual problem! I eventually wrote a little program to simulate it.
I’m going to imagine two scenario, both involving a pencil just kind of sitting around in space.
In the first verison, the pencil is just sitting there, and then you give it a bit of a nudge near the end, so it starts rotating around end-over-end. As it rotates around, it make a kind of circle in one spot.
Now do a second version, where the pencil is spinning around the long axis. Now give it the same kind of nudge. You might think that the pencil will make the same kind of circular motion, but be spinning around it’s axis to. But you’d be wrong, that’s not what it does. Instead, it will just kind of wobble.
If you don’t give them extra energy, all things actually always rotate around a single axis. It’s just what they do.
(Unless I’m wrong, of course, but I don’t think I am)
Let’s talk about vectors.
If we have a vector in the x direction and the one in the y direction, we can add them together, and we get one pointing at a diagonal.
It doesn’t make sense if we could have a vector pointing in two directions at once, it’s just the sum of two other vectors.
Now, rotational velocity can also be described as a vector. Look at the way its rotating and curl the fingers on your right hand, leaving your thumb extended. Your fingers should curl the same direction as the rotation. The way your thumb points uniquely describes the direction of the vector of the rotational velocity. Note how it points along the axis on which the object is rotating.
Since we can describe the rotation around an axis, adding a rotation around another axis lets us add the two vectors together, and the new axis of rotation will point in the direction of that new vector.
For totally free motion, you only need translational motion in 3 axes and rotational motion in 3 axes. This is called 6 degrees of freedom.
Port/starboard
Fore/aft
Ventral/dorsal
Yaw
Pitch
Roll
These are the 6 directions
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