Polar Kinematics - omega vs. theta_dot?

  • #1

Main Question or Discussion Point

Are ω and [itex]\dot{θ}[/itex] the same in a polar kinematics?

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

If they are not the same, what is the physical meaning of [itex]\dot{θ}[/itex]?
 

Answers and Replies

  • #2
Doc Al
Mentor
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Are ω and [itex]\dot{θ}[/itex] the same in a polar kinematics?

I know ω is angular speed (rad/s) and it seems to me that [itex]\dot{θ}[/itex] would be the same, but in the context of rotation in polar coordinates where v = [itex]\dot{r}[/itex][itex]\widehat{r}[/itex]+ r[itex]\dot{θ}[/itex][itex]\widehat{θ}[/itex], v = rω, and vθ = r[itex]\dot{θ}[/itex], that doesn't seem to be true.
What you have called v and vθ seem to be the same thing.
 
  • #3
285
79
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 = [itex]\dot{θ}[/itex] = dθ/dt (a scalar speed value).

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

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