The virial theorem

1. The problem statement, all variables and given/known data
In the Virial theorem The scalar virial G is defined by the equation:
$$G=\vec{p}\cdot \vec{r}$$
Where ##\vec{p}## is the momentum vector and ##\vec{r}## the location vector.
When i take the mean of the derivative ##\bar{\dot{G}}## over a whole period T it equals 0. why?

2. Relevant equations
$$\vec{p}\cdot \vec{r}=(mv)\cdot \cos \theta \cdot r$$

3. The attempt at a solution
I understand this scalar product is zeroed during one period, but why?

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