Sanity check please -- Load cable swinging outward on a rotating crane

[Thickmax]

Homework Statement

Please can my work be sanity checked? I think I'm on the right lines

Relevant Equations

See below

So I know

Fcp=-m*w^2*r

So from the equation -m*w^2*r=m*g*tan(theta)

r = r1+r2

so to rewrite

-m*(w^2)*(r1+r2)=m*g*tan(theta)
So
r1+r2=(m*g*tan(theta))/-m*(w^2)

r1=((m*g*tan(theta))/-m*(w^2)) - r2

Am I doing this nearly correct?

 

[haruspex]

Am I doing this nearly correct?

Yes, but one of your variables is not in the list of those allowed in the answer. Can you see a way to get rid of it?

 

[Lnewqban]

Shouldn't $r_2$ be directly proportional to $\omega^2$?

 

[Delta2]

Shouldn't $r_2$ be directly proportional to $\omega^2$?

No the crane rotates around its base column, the radius of rotation is $R=r_1+r_2$ not just $r_2$.

 

[Thickmax]

Yes, but one of your variables is not in the list of those allowed in the answer. Can you see a way to get rid of it?

I can indeed! m's are overrated! Thank you for the confirmation