# Can an object travelling in a straight line have angular momentum?

1. Apr 28, 2012

### khoivu

I have seen solutions of many problems in which an object going in straight line has angular momentum, especially those use conservation of angular momentum. For example, a person throws a ball at a rod that is hung vertically at one end. The solution says that at the moment before the ball hits the rod, the ball's angular momentum is L=mvl. However, how can the ball acquire such angular momentum when it's not travelling in a curve path which has a fixed radius to the origin? In my understanding, when an object goes in a straight line, it can not maintain a fixed value for r with respect to the origin on its way. So the r would be changing constantly and becomes a variable. Also, as the r changes its magnitude and direction, so do the angle θ between r and v.
Can anyone help me with this question? Thanks :)

2. Apr 28, 2012

### K^2

The angular momentum isn't just mvr, it's mvr sinθ, where θ is the angle between r and v. That quantity actually remains constant for an object moving in a straight line. As r increases, sinθ decreases. If you want to get a bit more technical, angular momentum is a vector quantity, and is given by L=mr×v. But the magnitude of that cross product depends on sinθ as described above.

Angular momentum isn't really jut about rotation. It's easier to understand in cases with rotation, but any kind of vector field has a moment around a fixed pivot. If you take momenta of various particles, the moment of momentum is the angular momentum. And it works out that both the total momentum and the total angular momentum are conserved quantities. In fact, you can derive one from the other using some symmetries.

3. Apr 28, 2012

### sweet springs

Hello.

Value of angular momentum depends on where the origin of the coordinate you set.
For example the origin is on the line of straight motion, the value is zero.
However, the origin is off the line, the value is positive or negative constant.

Regards.