Learning Objective: Calculate tension at the top and bottom of vertical circular motion, and determine the minimum speed needed to maintain circular motion.

Vertical Circle Calculator

Speed at Top
0 m/s
Min Speed (top)
0 m/s
Tension at Top
0 N
Tension at Bottom
0 N
Speed at top is below minimum! The object will fall before reaching the top.
Tbottom = mg + mv²/r   Ttop = mvtop²/r − mg   vmin = √(gr)

Four-Position Diagram

T mg v T mg v T mg v T mg v Top Bottom Left Right h = 2r h = 0
→ T = Tension   → mg = Weight   → v = Velocity