Step 1: Draw the free body diagram showing ALL real forces (no centrifugal force in inertial frame).

Step 2: Choose coordinates — radial (toward centre) and tangential (along the circle).

Step 3: Apply Newton's second law:

• Radial: F_{net}_{radial} = $mv^2$/r (toward centre)
• Tangential: F_{net}_{tangential} = m*$\frac{dv}{dt}$

Step 4: Use energy conservation to relate speeds at different positions (for vertical circles): \frac{1}{2}$$mv_1^2 + $mgh_1$ = \frac{1}{2}$$mv_2^2 + $mgh_2$.

Step 5: Apply the specific condition:

• Complete loop: T >= 0 at the top
• String breaks: T = $T_{max}$
• Leaves surface: N = 0
• Banking: resolve N and friction into radial and vertical components

Step 6: Check units and limiting cases (e.g., mu = 0, theta = 0).