'Direction' of Angular Momentum

[frankhawes]

Hello everyone!

I'm going to uni in October and I'm brushing up on my mechanics before I go.
I've just got to a bit that has confused me before and has confused me again now:

When you have a rotating object, say it is rotating in front of you in a vertical plane and it is rotating anti-clockwise then I think I'm correct in saying that the direction of the angular momentum would be towards you.
I don't understand this, as far as I am aware there is nothing physical coming towards me...
Is this is just convention? If it is then why has the convention arisen, I can't see the convenience in arbitrarily giving the angular momentum a direction.

Please can someone help me :)
Thanks in advance,
Frank

 

[A.T.]

I don't understand this, as far as I am aware there is nothing physical coming towards me...

The axis of rotation is pointing at you. See angular velocity, which is also vector.

Is this is just convention?

Yes.

If it is then why has the convention arisen,

To make the math more convenient.

I can't see the convenience in arbitrarily giving the angular momentum a direction.

How would you distinguish rotations around different axes, if angular momentum didn't have a direction?

 

[frankhawes]

Then do some math, and try to find a more convenient convention.

Thanks for your quick reply.
I have my same confusions over angular velocity.
Do you have any suggestions about what 'math' I can try? I agree this is probably a good way of developing an intuition for the convention.

Thanks again,
Frank

 

[A.T.]

I have my same confusions over angular velocity. Do you have any suggestions about what 'math' I can try?

Try to mathematically describe arbitrary rotations. How would you distinguish rotations around different axes, if angular velocity didn't have a direction?

 

[frankhawes]

Try to mathematically describe arbitrary rotations. How would you distinguish rotations around different axes, if angular velocity didn't have a direction?

Okay, Thank you.

 

[rcgldr]

Consider the alternative of describing an angular quantity, such as angular position, angular velocity, angular acceleration, angular inertia, or torque with something other than a vector, such as some type of plane. You'd have the complication of mathematically describing the plane and trying to perform math such as torque = angular inertia x angular acceleration. Using vectors to describe angular quantities eliminates this issue.

As mentioned above, the usage of right hand rule (so that counter clockwise rotation is a vector pointed towards you as opposed to away from you) is a convention, but it corresponds to some conventions used in electronics, such as positive or negative charge, the direction of a magnetic field, and it's relationship to charges moving perpendicular to the magnetic field.

 

[frankhawes]

Consider the alternative of describing an angular quantity, such as angular position, angular velocity, angular acceleration, angular inertia, or torque with something other than a vector, such as some type of plane. You'd have the complication of mathematically describing the plane and trying to perform math such as torque = angular inertia x angular acceleration. Using vectors to describe angular quantities eliminates this issue.

As mentioned above, the usage of right hand rule (so that counter clockwise rotation is a vector pointed towards you as opposed to away from you) is a convention, but it corresponds to some conventions used in electronics, such as positive or negative charge, the direction of a magnetic field, and it's relationship to charges moving perpendicular to the magnetic field.

Thank you, this makes sense :)