# Does every moving object have orbital angular momentum?

Hello,

in classical physics orbital angular momentum is defined as the cross product of the position vector 'r' and the momentum 'p'. A friend told me that all moving objects must have orbital angular momentum (even if it is moving along a straight line). That statement confuses me a lot, because mathematically the vector product can become zero.

Suppose, we fix a coordinate system and our object is moving such that the position r and the momentum p are parallel. Then, mathematically, the angular momentum is zero. But, if we shift the origin of the coordinate system, then the orbital angular momentum suddenly becomes nonzero. It seems to me, that the angular momentum depends on our choice of coordinate system. Is that right? Maybe my friend had in mind something like: We can always choose a coordinate system, such that the orbital angular momentum of a moving object is not zero. This statement somehow seems to be wrong, because I would not expect a physical property to depend on our choice of coordinate system. Can someone explain where my mistakes are?

Best wishes

mfb
Mentor
All objects (with non-zero mass) have angular momentum in some but not all reference frames.
This statement somehow seems to be wrong, because I would not expect a physical property to depend on our choice of coordinate system.
A lot of things depend on your reference frame. Velocity depends on it - is that odd? Energy depends on it as well, and so on.

PeroK
Homework Helper
Gold Member
2021 Award
Hello,

in classical physics orbital angular momentum is defined as the cross product of the position vector 'r' and the momentum 'p'. A friend told me that all moving objects must have orbital angular momentum (even if it is moving along a straight line). That statement confuses me a lot, because mathematically the vector product can become zero.

Suppose, we fix a coordinate system and our object is moving such that the position r and the momentum p are parallel. Then, mathematically, the angular momentum is zero. But, if we shift the origin of the coordinate system, then the orbital angular momentum suddenly becomes nonzero. It seems to me, that the angular momentum depends on our choice of coordinate system. Is that right? Maybe my friend had in mind something like: We can always choose a coordinate system, such that the orbital angular momentum of a moving object is not zero. This statement somehow seems to be wrong, because I would not expect a physical property to depend on our choice of coordinate system. Can someone explain where my mistakes are?

Best wishes

Angular momentum is defined relative to a point. You can consider the angular momentum of a particle relative to any point; hence, the value of angular momentum depends on your choice of point. The Moon, for example, has angular momentum relative to the Earth, and also a different angular momentum relative to the Sun, for example.

In answer to your other question: a particle moving in a straight line has non-zero angular momentum relative to any point not on its path.

• HastiM
DrClaude
Mentor
all moving objects must have orbital angular momentum (even if it is moving along a straight line)s
That also caused me problems when I first heard it. The way I visualised it to help me wrap my head around it is like this:

Imagine that you are looking at an object moving in a straight line. Unless it is moving straight towards you or away from you, to keep looking at it without changing place you need to continuously turn. Therefore, from you vantage point, the object has some form of rotation, it has angular momentum. #### Attachments

• HastiM
dRic2
Gold Member
An other way to think about it (that absolutely struck me) is this:

Imagine that you are looking at an object moving in a straight line.

at constant speed: It will keep moving in a straight line (at constant speed) because of inertia. Or you can say that it will keep moving in a straight line (at constant speed) because of conservation of angular momentum. ;)