Conical Pendulum

About this simulation

Conical Pendulum shows a ball whirling on a string so the string traces a cone. Students change the spin rate, the string length and the mass, and can show tension, weight and centripetal force arrows. Readouts give the cone angle, tension, centripetal force and the period and speed. The sim demonstrates that the vertical part of the tension cancels weight while the horizontal part provides the centripetal force, and that spinning faster lifts the ball higher.

What students can explore

Raise Spin rate and watch the Cone angle readout grow.
Lower Spin rate until the ball just hangs and find the minimum spin.
Turn Force arrows on and compare the tension arrow with the weight arrow.
Double the Mass and check how Tension and Centripetal force change.
Change String length and compare the Period readout with your prediction.

Learning objectives

1Resolve string tension into vertical and horizontal components.
2Identify the centripetal force in a conical pendulum.
3Explain why a faster spin gives a larger cone angle.
4Use m times omega squared times r for centripetal force.

Questions teachers ask

Is the Conical Pendulum simulation free?

Yes. It is free, requires no sign-up and runs in any modern browser, including whiteboards, tablets and Chromebooks.

What provides the centripetal force?

The horizontal component of the string tension. The vertical component balances the weight, so the ball stays at the same height while circling.

How do I use it?

Move the sliders for spin rate, string length and mass, and switch Force arrows on. The cone angle eases to its new value. Read tension and centripetal force from the readouts.

Does the mass change the cone angle?

No. Mass cancels from the equations, so the angle depends only on spin rate, string length and gravity. Tension, however, grows with mass.

Embed this simulation

Drop it into your LMS, blog, or class site — free.

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