# Homework Help: Angular Velocity Keeping Strings Taut

1. Nov 18, 2012

### newtophysics2

1. The problem statement, all variables and given/known data
A ball of mass m is attached by two strings to a vertical rod. as shown in the diagram attached. The entire system rotates at constant angular velocity ω about the axis of the rod.

a)Assuming ω is large enough to keep both strings taut, find the force each string exerts on the ball in terms of ω, m, g, R, and θ.

b)Find the minimum angular velocity, θ_min for which the lower string barely remains taut.

2. Relevant equations
F_centripetal=mv2/r
F=ma

3. The attempt at a solution
A) To keep the strings taut, the net force in the y-axis and the x-axis have to both equal 0. I used forces and tension, but my answer didn't contain ω, but I feel like it should...
T1 tension is making θ angle with the vertical
T1cosθ along vertical upward
T1sinθ along horizental i.e towards the center of the circular path
applying ΣFy =0 ΣFx =0
T1cosθ=mg
T1=mg/cosθ
T1sinθ+T2=mv2/R
T2=mgsinθ+mv2/R

B) I would solve for v from the equations above, but the question doesn't say that I can use T (tension) in my answer...

What am I doing wrong in this problem? Thanks in advance!

#### Attached Files:

• ###### Diagram.png
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2. Nov 18, 2012

### Spinnor

Velocity and angular velocity are related by,

v = ωR

Also,

b)Find the minimum angular velocity, θ_min for which the lower string barely remains taut.

b)Find the minimum angular velocity, ω_min for which the lower string barely remains taut.

3. Nov 18, 2012

### newtophysics2

Ok, thanks! So did I do part A correctly? And for part B, do I just set T2=0 and then substitute v=ωR to solve for ω?

4. Nov 18, 2012

### haruspex

No. The complete equation is Fnet=ma. There is an acceleration, so the net force must provide that.

5. Nov 18, 2012

### newtophysics2

How do I determine the acceleration? So is my solution wrong?

6. Nov 18, 2012