Homework Help: Angular momentum equation

1. Aug 26, 2011

Pollywoggy

1. The problem statement, all variables and given/known data

I found this in Goldstein, Poole, and Safko and have seen it in other books. What I don't understand is how the equation gets from the second expression to the third; specifically, why is the m divided by two in the last expression? I am at a loss on this but I know it is not a typo.

2. Relevant equations
$$\int \mathbf{F} \cdot d\mathbf{s} = m \int \frac{d\mathbf{v}}{dt} \cdot \mathbf{v} dt = \frac{m}{2} \int \frac{d}{dt}(v^2)dt$$

2. Aug 26, 2011

Staff: Mentor

$$\frac{d \; v^2}{dt} = 2 v \frac{d v}{dt}$$
so to make this simply $\frac{dv}{dt} v$ it needs to be divided by two.

3. Aug 26, 2011

Pollywoggy

Thanks, I knew it was something simple that I just could not see.