# I Difference between Moment-of-Momentum and Angular Momentum

1. Aug 21, 2016

### tomwilliam2

I've been reading a book that talks about the angular momentum of an extended body around a point 0 (H_0) being made up of the moment-of-momentum of an equivalent particle (representing the total mass at the centre of mass) with respect to the point 0 and the angular momentum around the centre of mass, C:
$\mathbf{H}_0 = M\mathbf{h}_0 + \mathbf{H}_C$
I've never seen this second term on the RHS before. Is it basically saying that there is the angular momentum of the e.p. with respect to the origin, but then there's also the angular momentum of the individual particles in the extended body around the centre of mass?

Last edited: Aug 21, 2016
2. Aug 22, 2016

### nasu

So what is your question? This decomposition of the total angular momentum is quite standard.
But what is "moment-of-momentum"?

3. Aug 22, 2016

### tomwilliam2

Thanks. My question was what each of the terms of the RHS corresponded to. It was my understanding that the first term related to the angular momentum of the equivalent particle with respect to the origin, while the second term was the angular momentum of the individual particles around the centre of mass of the extended object. Is that a correct interpretation?
Moment-of-momentum is defined (by the author of the book I'm reading) as
$m\mathbf{h}_0 = \mathbf{r} \times m\mathbf{v}$
"moment-of-momentum is often loosely referred to as 'angular momentum' $\mathbf{H}_0$. This can lead to some confusion. Only in special cases are the two identical, such as when there is only one particle."

4. Aug 22, 2016

### nasu

Yes, these are the meanings of the terms.
If you want to see where they come from, look up "angular momentum of a system of particles".
For example here, see under "colelction of particles":
https://en.wikipedia.org/wiki/Angular_momentum#Collection_of_particles

Yes, you are right. The "moment of momentum makes sense. It is the moment of the linear momentum. It is just unusual.
Is the book you quote in English or you translate from a different language?

5. Aug 23, 2016

### tomwilliam2

Thanks again.
The book is in English ("Spacecraft Systems Engineering" by Fortescue, Swinerd and Stark).