Show magnitude of velocity vector in polar coordinates

[leonne]

Homework Statement

In Cartesian coordinates the magnitude of the velocity vector squared is
|v|^2=V*V= Vx^2 +Vy^2 =(dx/dt)^2+(dy/dt)^2
Show that in polar coordinated
|v|^2= Vr^2 +V@ ^2

Homework Equations

The Attempt at a Solution

Not really sure what the question is asking me to do, but i am guessing to convert (dx/dt)^2+(dy/dt)^2 into polar? or do i need to do it for all of it?

Well I got dy/dt=(dr/d@) sin@+rcos@ and dx/dt=(dr/d@) cos@-rsin@

Is this right? Were do i go after this?

Thanks

 

[kuruman]

It is not right.
If x = r cosθ, then
(dx/dt) = (dr/dt) cosθ - r sinθ (dθ/dt). That's the chain rule of differentiation.

Find a similar expression for (dy/dt), square each expression then add.

 

[leonne]

cool thanks for info ill try it out tomorrow