Period of a rotating mass held by two strings

[limekiwi]

Homework Statement

The 4.00kg block in the figure (Intro 1 figure) is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in the diagram and the tension in the upper string is 82.0 N.

Homework Equations

a) What is the tension in the lower cord?
b) How many revolutions per minute does the system make?
c) Find the number of revolutions per minute at which the lower cord just goes slack.

The Attempt at a Solution

a) I need to focus on the y-component so..
T1 cos$$\theta$$ - T2 cos$$\theta$$ - mg = 0
I find $$\theta$$ by taking the triangle formed by the rod and two strings...

cos$$\theta$$ = 1/1.25
With all this info.. I can find T2. Correct?

b) I know the formula for T is T = (2$$\pi$$r) / V... or T = 2$$\pi$$*[(Lcos$$\theta$$)/g]^1/2
Do I actually use this formula? I am a bit confused since later I have to find T when the lower cord slacks. Can someone clear this up for me?

 

[Redbelly98]

a) ... With all this info.. I can find T2. Correct?

Yes, correct.

b) I know the formula for T is T = (2$$\pi$$r) / V... or T = 2$$\pi$$*[(Lcos$$\theta$$)/g]^1/2
Do I actually use this formula? I am a bit confused since later I have to find T when the lower cord slacks. Can someone clear this up for me?

What equation involves force and circular motion?