Polar Kinematics - omega vs. theta_dot?

[mechEstudent]

Are ω and $\dot{θ}$ the same in a polar kinematics?

I know ω is angular speed (rad/s) and it seems to me that $\dot{θ}$ would be the same, but in the context of rotation in polar coordinates where v = $\dot{r}$$\widehat{r}$+ r$\dot{θ}$$\widehat{θ}$, v = rω, and v_θ = r$\dot{θ}$, that doesn't seem to be true.

If they are not the same, what is the physical meaning of $\dot{θ}$?

 

[Doc Al]

Are ω and $\dot{θ}$ the same in a polar kinematics?

I know ω is angular speed (rad/s) and it seems to me that $\dot{θ}$ would be the same, but in the context of rotation in polar coordinates where v = $\dot{r}$$\widehat{r}$+ r$\dot{θ}$$\widehat{θ}$, v = rω, and v_θ = r$\dot{θ}$, that doesn't seem to be true.

What you have called v and v_θ seem to be the same thing.

 

[tygerdawg]

I could be wrong...

It seems your v is the instanteous velocity vector of a point in space in polar coordinates. The r components describe the motion of a point along the axis of the radius r. The θ components describe the motion of the point about the axis of rotation of θ.

Therefore ω = $\dot{θ}$ = dθ/dt (a scalar speed value).

Symbolic terminology is confusing. Drinking more beer usually corrects this.