3.3.3—Circular acceleration

For a particle moving at constant speed in a horizontal circle, the resultant horizontal or radial force must equal mv²/r. Vertical forces must separately balance if the height is constant.

Resolve the actual forces—tension, normal reaction, friction or a component of weight—before setting their radial resultant equal to mv²/r. The centre direction changes around the circle.

For a conical pendulum, the vertical component of tension balances mg while the horizontal component supplies m v²/r; using all of T as centripetal force is wrong.

“Centripetal force” is a role played by the resultant inward force, not an extra force to add to the free-body diagram.