Vertical Circular Motion

Overview

At BOTTOM of loop: centripetal direction is upward. N − mg = mv²/r → N = mg + mv²/r. Normal force is greater than weight — you feel 'heavier'. At TOP of loop: centripetal direction is downward. T + mg = mv²/r (string) or mg − N = mv²/r (track). Minimum speed at top: set T = 0 (string) or N = 0 (track) → v_min = √(gr). Car over a hill: mg − N = mv²/r → N = m(g − v²/r). Car loses contact when N = 0: v_max = √(gr). Key: always identify which forces point TOWARD the centre at that position.