Distribution of Energy: Deriving T from m, V, v0, & θ

[abccdef125]

Hi,
i´m reading Landau´s mechanics and in the 4th chapter in the part disintegration of particles (16) i can´t figure out the following thing. We have a function T=(1/2)m(V²)+(1/2)m(v₀²) + mVv₀cos(θ) , where V and v₀ are constant in this problem. We also know the distribution of θ which is (1/2)sinθdθ. The goal is to get a distribution of T. Could you please explain to me how to get it? The book derives it in a way i can´t understand. Thanks in advance.

 

[Simon Bridge]

Welcome to PF;
The trick is to understand what the distribution means - i.e. what would the "distribution of T" tell you, once you have it? What is the "distribution of $\small \theta$" telling you?

 

[abccdef125]

Thanks, i went through it once more with your advice in mind and i finally understand it.

 

[Simon Bridge]

Well done :)

The next step is to find someone who is struggling and see if you can get them to understand.