# I Exactly why are these two expressions similar?

1. Aug 22, 2016

### snoopies622

So if angular momentum

$L = m r^2 \dot {\theta}$

and we take the first time derivative

$\frac {d}{dt} L = 2mr \dot {r} \dot {\theta} + m r^2 \ddot {\theta}$

the first term looks similar to the Coriolis force $2m( \bf {v} x \bf { \dot {\theta} } )$
but I can't figure out why. Of course they both have to do with rotation so I'm guessing that it's not a coincidence, but I can't quite arrive at the exact mathematical connection between the two expressions.

Would anyone like to help me out?

2. Aug 22, 2016

### Staff: Mentor

Doesn't look similar to me. Cross product vs. no cross product, and then you have the additional radius in one equation.

3. Aug 22, 2016

### snoopies622

Yes, I should have expressed angular momentum and its time derivative as vectors as well, then we'd have cross products on both sides.

For the moment my hunch reasoning goes like this:

1.) In a rotating frame of reference, a "floating by" object (one not acted on by external forces) is subject to two fictious forces — centrifugal and Coriolis.

2.) A force causes a change in (linear) momentum.

3.) Angular momentum is a function of linear momentum, therefore a change in one is likely to effect a change in the other.

4.) The time derivative of angular momentum expresses a change in angular momentum.

So there's a connection. Hopefully this is enough to lead me through the mathematics and see if the similarity of the two terms mentioned in the OP is a coincidence or not.