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?