Deriviate proof d/dt[r (v a)]= r(v a)

[agentnerdo]

Hey guys, I really do not even know how to get this question started.

Homework Statement

\frac{d}{dt}[r (v x a)] = r (v x a)

the last a is supposed to have a period on top

as such it is \frac{d}{dt}[r (v x a)] = r (v x \frac{d}{dt}a)

d, v, and a are position, velocity, and acceleration

the last a, after the = sign is d/dt of a, as mentioned above

The Attempt at a Solution

I do not even know how to start...I tried doing different degrees of deriviatives of both left and right sides but, it seems like I need to get ride of one unit of /s (time).

 

[agentnerdo]

that was an epic fail on trying to use brackets...


derivative of [r (v times a)] = r ( v times a*)

a* is the derivative of a.

question asks to prove that both sides are equal.

 

[RoyalCat]

Simply apply the chain rule and remember that the cross product of a vector with itself is 0, and that $$\vec a \cdot (\vec a \times \vec b)=0$$ (Convince yourself this is true, because a x b is perpendicular to a, and the dot product of a vector with another vector to which it is orthogonal, is 0)