Lab: The Conical Pendulum

A conical pendulum looks like a normal pendulum except the bob never swings back and forth through the bottom. Instead it moves in a steady horizontal circle while the string sweeps out a cone shape, tilted at some constant angle theta from vertical. That tilt is not optional. The bob is accelerating toward the center of the circle, so something has to supply a net force pointing inward. Gravity alone points straight down and cannot do that, so the string leans out, giving tension a sideways component that points toward the center.

Draw the free-body diagram: two forces act on the bob, gravity mg straight down and tension T along the string. Split T into components. The vertical piece, T cos(theta), balances gravity, since the bob does not move up or down. The horizontal piece, T sin(theta), is unbalanced and points toward the center of the circle, so it equals the centripetal force mv²/r. Dividing these two equations cancels T and m, leaving tan(theta) = v²/(rg). Combine that with the geometry of the cone, where r = L sin(theta), and the algebra simplifies beautifully: the period T = 2 π √(L cos(theta) / g). Longer strings and smaller angles both make the swing slower.

This lab ties directly to circular motion ideas elsewhere in the unit: centripetal force is never a new force, just the net result of real forces, here tension and gravity, pointing inward. It also previews banked turns and orbits, where a tilted surface or gravity itself plays the same role tension plays here.