How Does Tension in a String Behave in Zero Gravity?

[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$$_{r}$$ $$\widehat{r}$$ + F$$_{\phi}$$ $$\widehat{\phi}$$

So I believe my tension force is just F$$_{r}$$ ?

and N2L: F= m(F$$_{r}$$ $$\widehat{r}$$ + F$$_{\phi}$$ $$\widehat{\phi}$$) ?

(for some reason my subscripts are appearing as superscripts)

 

[Doc Al]

So I believe my tension force is just F$$_{r}$$ ?

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

 

[Oblio]

I found in my text that

"F$$_{r}$$ would be the tension in the string and F$$_{\phi}$$ 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$$_{r}$$?

 

[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.

$$F_{r}$$ (F within tex brackets) versus F$$_{r}$$ (F outside of brackets)