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*(dv/dt)

Step 4: Use energy conservation to relate speeds at different positions (for vertical circles): (1/2)mv_1^2 + mgh_1 = (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).