UCM:

• v = romega, omega = 2pi/T = 2pif
• a_c = v^2/r = r*omega^2, F_c = mv^2/r

Vertical Circle (string, length L):

• Top: T + mg = mv^2/L; min v = sqrt(gL)
• Bottom: T - mg = mv^2/L; min v = sqrt(5gL)
• T_bottom - T_top = 6mg

Vertical Circle (rod):

• Min v at top = 0; min v at bottom = 2*sqrt(gL)

Banked Road:

• No friction: v = sqrt(rg*tan(theta))
• Max speed: v_max = sqrt(rg(tan(theta)+mu)/(1-mu*tan(theta)))
• Min speed: v_min = sqrt(rg(tan(theta)-mu)/(1+mu*tan(theta)))

Flat road: v_max = sqrt(mu*rg)

Conical pendulum: T = 2pisqrt(L*cos(theta)/g)

Non-uniform: a_net = sqrt(a_c^2 + a_t^2)