Finding the tension in a circular pendulum without radius or angle.

1. The problem statement, all variables and given/known data

Some kid is playing with a yoyo of mass m. The yoyo string is let out to length L, and is spun in a horizontal circle at a constant rate of ω. The yoyo string makes an angle of θ with the horizontal

m = 39 grams = 0.039 kilgrams
L = 46cm = 0.46m
ω = 3 rads/sec

Calculate the tension in the string in Newtons.

2. Relevant equations

Tx = Tcosθ = mω2r = mv2/r

Ty = Tsinθ = mg = 0.3822N

r = L cosθ

h = L sinθ

3. The attempt at a solution

The vertical component of the tension was easy, the only force acting in this direction is gravity with a force of m*g newtons.

The horizontal component is more confusing… Since the height, radius and length of string (hypotenuse) form a right triangle, the lengths of sides should correspond to the ratios on them.

But I don’t seem to know the vertical length, just the force’s magnitude.
I’m trying to solve for the hypotenuse’s force’s magnitude, but only know the length.
And I don’t seem to know anything at all about the horizontal length/radius of the circle has been formed or its force.

So using Fx^2 + Fy^2 = T^2 or x^2 + y^2 = L^2 is out. The angular velocity seems hard to use without knowing the radius.

Whats a step that takes me to finding the tension, radius, or θ?

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