tension force

Oblio

an astronaut in gravity free space is twirling a mass m on the end of a string of length R in a circle, with constant angular velocity. Write down Newtons second lasw in polar coordinates and find the tension of the string.


What makes up F(t) without acceleration and gravity? I'm confused.

Doc Al

There might not be gravity, but there's certainly acceleration. (Hint: Circular motion.)

Oblio

I see that the net force can be written as:

F = F[tex]_{r}[/tex] [tex]\widehat{r}[/tex] + F[tex]_{\phi}[/tex] [tex]\widehat{\phi}[/tex]

So I believe my tension force is just F[tex]_{r}[/tex] ?

and N2L: F= m(F[tex]_{r}[/tex] [tex]\widehat{r}[/tex] + F[tex]_{\phi}[/tex] [tex]\widehat{\phi}[/tex]) ?

(for some reason my subscripts are appearing as superscripts)

Doc Al

OK. And since the angular velocity is constant, what's the tangential force?

Oblio

I found in my text that

"F[tex]_{r}[/tex] would be the tension in the string and F[tex]_{\phi}[/tex] the force of air resistance retarding the stone in the tangential direction."

Do I need to account for air resistance in the tension or is it simply F[tex]_{r}[/tex]?

Oblio

( On my computer anyways, subscripts are still appearing as superscripts, not sure why )

Doc Al

They are in free space--no air, no air resistance.

[tex]F_{r}[/tex] (F within tex brackets) versus F[tex]_{r}[/tex] (F outside of brackets)