A conical pendulum is a mass suspended from a point that traces out a horizontal circle. By balancing the weight with the tension in the string, determine the speed of the bob.

Draw a free-body diagram for the mass with the pendulum suspended at an angle θ to the vertical. The tension in the rope is T and the radius of the circle is r.
Firstly, resolve horizontal forces and equate to the centripetal force: Tsinθ = mv^2/r (1), where v is the speed of the bob . Resolve vertical forces Tcosθ-mg = 0 --> Tcosθ = mg (2). Divide (1) and (2) to eliminate T --> sinθ/cosθ = tanθ = v^2/rg. Rearrange for v to get v = (rgtanθ)^1/2.