# Does every moving object have orbital angular momentum?

• HastiM
In summary: Now imagine that you are looking at the object from some other point in space.If you shift your perspective so that the object is moving away from you, then its angular momentum will be increasing.If you shift your perspective so that the object is moving towards you, then its angular momentum will be decreasing.

#### HastiM

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

All objects (with non-zero mass) have angular momentum in some but not all reference frames.
HastiM said:
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.

HastiM said:
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
HastiM said:
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.

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

DrClaude said:
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. ;)

## 1. What is orbital angular momentum?

Orbital angular momentum is a property of a moving object that describes its rotational motion around a fixed point or axis. It is a vector quantity that depends on the mass, speed, and distance of the object from the axis of rotation.

## 2. Does every moving object have orbital angular momentum?

Yes, every moving object has orbital angular momentum as long as it is rotating or moving in a curved path around a fixed point or axis. This includes objects in circular orbits, such as planets around a star, as well as objects with rotational motion, such as a spinning top.

## 3. How is orbital angular momentum different from linear momentum?

Orbital angular momentum and linear momentum are both measures of an object's motion, but they describe different aspects of that motion. Linear momentum describes the object's straight-line motion, while orbital angular momentum describes its rotational motion around a fixed point or axis.

## 4. Can an object have zero orbital angular momentum?

Yes, an object can have zero orbital angular momentum if its motion is purely linear, meaning it is moving in a straight line with no rotational component. This can occur when an object is moving in a straight path or at a constant speed in a circular orbit.

## 5. How is orbital angular momentum conserved?

Orbital angular momentum is conserved, meaning it remains constant, as long as there is no external torque acting on the object. This is known as the law of conservation of angular momentum. If there is no external torque, then any changes in an object's rotational motion will be offset by equal and opposite changes in its linear motion, and vice versa.