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.

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.

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

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