Possible webpage title: Understanding Multiple Axes of Rotation in Objects

[Hoophy]

So I am having trouble with this one, I was wondering if an object could have more than one axis of rotation. More than one axis of rotation goes against what I think is possible until I thought about a coin, at which point I was stumped, if the coin was rotating in the way a coin rotates when you spin it like a spinning top but was also spinning in a way in which it resembles a wheels rotation BOTH AT THE SAME TIME, would it have two axis of rotation? If so how is that possible and If not what would the single axis look like? Also for simplicity sake imagine that the coin is rotating in outer space. I am so utterly confused. I would really appreciate an explanation of why this is the way it is. Thank you for your time.

 

[berkeman]

So I am having trouble with this one, I was wondering if an object could have more than one axis of rotation. More than one axis of rotation goes against what I think is possible until I thought about a coin, at which point I was stumped, if the coin was rotating in the way a coin rotates when you spin it like a spinning top but was also spinning in a way in which it resembles a wheels rotation BOTH AT THE SAME TIME, would it have two axis of rotation? If so how is that possible and If not what would the single axis look like? Also for simplicity sake imagine that the coin is rotating in outer space. I am so utterly confused. I would really appreciate an explanation of why this is the way it is. Thank you for your time.

Sure. Gyroscopes do it all the time...

EDIT -- But see post #6 below for how to add the various rotations vectorially.

https://upload.wikimedia.org/wikipedia/commons/e/e2/3D_Gyroscope.png

 

[wrobel]

Theorem. Suppose that a rigid body has a fixed point and moves with nonzero angular velocity: $\boldsymbol \omega\ne 0$. Then at each moment of time there exists a unique line belonging to the rigid body such that the velocity of any point of this line is equal zero.

This line is referred to as axis of rotation

 

[olgerm]

if an object could have more than one axis of rotation.

No.

More than one axis of rotation goes against what I think is possible until I thought about a coin, at which point I was stumped, if the coin was rotating in the way a coin rotates when you spin it like a spinning top but was also spinning in a way in which it resembles a wheels rotation BOTH AT THE SAME TIME, would it have two axis of rotation?

It is analogues to how a car may move forward on road and same move to one side of road (change lane), but does not have 2 speed vectors.

 

[Hoophy]

I still do not understand. I don't know if the gyroscope applies to what I'm thinking, I meant a more "solid" object. How would an object rotate on 2 axis using the analogy of a coin? Imagine you are trying to explain this to a dummy. (That's me)

 

[A.T.]

If not what would the single axis look like?

If you know angular velocities around individual axes, you add them vectorially, to get the total angular velocity, which is parallel to the total axis of rotation
https://en.wikipedia.org/wiki/Angular_velocity
https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction

 

[anorlunda]

I still do not understand. I don't know if the gyroscope applies to what I'm thinking, I meant a more "solid" object. How would an object rotate on 2 axis using the analogy of a coin? Imagine you are trying to explain this to a dummy. (That's me)

How would you describe this?

 

[olgerm]

If so how is that possible and If not what would the single axis look like?

1. Take a coin and spin it the way you described.
2. Now take a ball and spin it the same way (same direction) as coin.
3. Notice 2 points on the ball, which are not moving(because of spinning).
4. Imagine line, which includes both of these points. This line is rotation axis.
5. Consider, that rotation axis of the coin is parallel with rotation axis of the ball.

 

[wrobel]

How would you describe this?

That's a good training question by the way. The coin loses its height because of the energy expires for friction of table. Consider an ideal model. The edge of coin does not slip on table's surface. It is not hard to write formulas and describe motion when the centre of coin runs by the horizontal circle and the absolute value of the center's velocity remains constant. For example, precise formulation may be as follows. Assume that we know absolute value of center's velocity and we know the angle between the table and the plane of coin. Find the radius of the circle which the center of coin describes. The radius of coin is also known.

 

[Hoophy]

So then would the two axis of any object have to be perpendicular to each other? And is there a limit to the number of axis an object can have at the same time?

 

[A.T.]

So then would the two axis of any object have to be perpendicular to each other? And is there a limit to the number of axis an object can have at the same time?

You can decompose the total angular velocity vector into arbitrary many vectors.

 

[Hoophy]

You can decompose the total angular velocity vector into arbitrary many vectors.

Could you please elaborate?

 

[A.T.]

Could you please elaborate?

https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Vectors#Vector_Addition

 

[anorlunda]

I hoped that the OP would respond to that video. I wanted to find out whether precession and rotation mean the same thing in his vocabulary.

 

[wrobel]

Standard fact.

Let $\Sigma$ stand for a rigid body that moves in space. Assume that its angular velocity does not vanish: $\boldsymbol\omega\ne 0.$

Theorem. There exists a unique line $\ell=\ell(t)\subset \Sigma$ such that for any point $B\in\ell$ it follows that the velocity $\boldsymbol v_B$ (of the point $B$) is parallel to the line $\ell$.
This line is parallel to the vector $\boldsymbol\omega$ and velocities of each point of this line are the same.
Moreover, if we know velocity of some point $O\in\Sigma$ then we can find a point $A\in\ell$ by the formula $\boldsymbol {OA}=\frac{1}{|\boldsymbol\omega|^2}\boldsymbol\omega\times\boldsymbol v_O.$

 

[Hoophy]

I think perhaps my question is way to broad and not very clear. I don't think that this can be explained to me because I need a more solid understanding of physics. Thanks for trying, I will do some more research on my own. Thanks again everybody.

 

[MrScott]

How would you describe this?

Nice video!
For this, external forces are being applied to the disc: it is in a gravitational field, applying downward force, and upward force is applied where the disc contacts the mirror.