Question

a small steel ball is attached and is spun in a horizontal circle of 30 cm radius as drawn below, where +z is upwards. What angle theta does the string make with the vertical when the ball is spun at a constant rate of 2 revolutions per second?

Answer 1

Fc = m v^2 / R horizontal force required to keep ball in circle

Fv = m g vertical force on ball due to weight

tan θ = Fc / Fv = v^2 / (R * g) angle from verticle

Circumference of circle = 2 π R

v = 4 π R distance traveled / sec

v^2 = 16 π^2 R^2

tan θ = 16 π^2 R / g

tan θ = 16 * π^2 * .3 / 9.80 = 4.83

θ = 78.3 deg from vertical