Loading [MathJax]/jax/output/HTML-CSS/jax.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Physics LibreTexts

41.3: The Conical Pendulum

( \newcommand{\kernel}{\mathrm{null}\,}\)

A conical pendulum is also similar to a simple plane pendulum, except that the pendulum is constrained to move along the surface of a cone, so that the mass m moves in a horizontal circle of radius r, maintaining a constant angle θ from the vertical.

For a conical pendulum, we might ask: what speed v must the pendulum bob have in order to maintain an angle θ from the vertical? To solve this problem, let the pendulum have length L, and let the bob have mass m. A general approach to solving problems involving circular motion like this is to identify the force responsible for keeping the mass moving in a circle, then set that equal to the centripetal force mv2/r. In this case, the force keeping the mass moving in a circle is the horizontal component of the tension T, which is Tsinθ. Setting that equal to the centripetal force, we have

Tsinθ=mv2r.

The vertical component of the tension is

Tcosθ=mg

Dividing Eq. 41.3.1 by Eq. 41.3.2,

tanθ=v2gr

From geometry, the radius r of the circle is Lsinθ. Making this substitution, we have

tanθ=v2gLsinθ

Solving for the speed v, we finally get

v=Lgsinθtanθ.


41.3: The Conical Pendulum is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

Support Center

How can we help?