# Conic Pendulum

Conic Pendulum

The conic pendulum is a system consisting of a mass hanging from a fixed point by a rope of length . It spins around the vertical with angle and with angular velocity . As the angular velocity increases, the angle from the vertical increases.

m

L

α

ω

α

The forces acting on the mass are the weight (red) and the tension (green), with resultant the centripetal force (magenta) equal to . The velocity vector is shown in yellow.

w

T

F

C

mLsin(α)

2

ω

v

Finally, the relation between the angular velocity and the angle is .

tan(α)=r

2

ω

g

For simplicity, the mass is taken as 1 kg and the radius equal to 1 m.