Home / Topics / Newton's Laws & Forces
Conical pendulum
Intermediate
A bob moving in a horizontal circle with the string tracing a cone.
T = 2π√(L cosθ/g)A bob on a string moves in a horizontal circle. T cosθ = mg and T sinθ = mv²/r give tanθ = v²/(rg) and period 2π√(L cosθ/g).
L = 1 m, θ = 30°: T ≈ 1.87 s.
The tension is bigger than the weight.
In more detail
A conical pendulum is a mass moving in a horizontal circle at the end of a string. Tension has a vertical component that balances weight and a horizontal component that provides centripetal force.
Real-world uses
- Centrifuges and some rotating amusement rides use this geometry.
- Textbook problems use the conical pendulum to link tension, angle and period.
- A conical pendulum like a rotating mixer or the swing ride at a fairground shows how a bob can trace a circle with the string at an angle.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Why doesn't the mass fall?
Because the vertical component of tension balances its weight, so it moves in a horizontal circle.
Does the period depend on mass?
No. It depends on the length and the angle of the string.
Why does a longer string give a slower rotation?
A longer string gives a longer period for the same angle, so the bob turns more slowly.
Related topics in Newton's Laws & Forces
Circular motion dynamics · Banking of roads · Vehicle on flat circular turn · Vertical circular motion · Loop-the-loop · Centrifugal force