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$\frac{L*cos(theta}{g}$)

Non-uniform: $a_{net}$ = sqrt($a_c^2$ + $a_t^2$)