How Is the Equilibrium Radius Determined in Rotational Spring Motion?

[Abarak]

Homework Statement

An object of mass M = 3.00 kg is attached to a spring with spring constant k = 132 N/m whose unstretched length is L = 0.170 m, and whose far end is fixed to a shaft that is rotating with an angular speed of omega = 2.00 radians/s. Neglect gravity and assume that the mass also rotates with an angular speed of 2.00 radians/s as shown.

http://img337.imageshack.us/img337/4482/6172alq9.jpg

Question:
Given the angular speed of omega = 2.00 radians/s, find the radius R($$\omega$$) at which the mass rotates without moving toward or away from the origin.

Homework Equations

$$k(R-L)$$
The amount of force a spring exerts is proportional to the distance it is stretched or compressed with respect to its equilibrium length ( L = 0.170 m in this case).

so...

$$F_{spring}(R)=k(R-L)$$

The Attempt at a Solution

"force a spring exerts is proportional to the distance it is stretched or compressed with respect to its equilibrium length" I am having problems with this part. I cannot figure out what the other side of the equation is.

I tried $$R-L=k(R-L)$$ but this does not work.

Any ideas?

-- Abarak

 

[Doc Al]

Apply Newton's 2nd law to the mass. Is it accelerating?

 

[Abarak]

From what I gather the object is not accelerating so Newton's 2nd law would not apply to this.

"force a spring exerts is proportional to the distance it is stretched or compressed with respect to its equilibrium length" I don't see how this would apply to Newton's second law or the other side of the equation:

$$? = k(R-L)$$

-- Abarak

 

[Doc Al]

From what I gather the object is not accelerating so Newton's 2nd law would not apply to this.

Sure it's accelerating--it's going in a circle! (Reread the chapter in your text about circular motion.)

 

[Abarak]

Oh snap! Talk about a lack of judgment. After applying Newton's 2nd Law everything worked like a charm.

Thanks again for the help Doc.

-- Abarak

 

[chenzo89]

how did you do this problem, because i have the same problem and its been bugging me like crazy.