Work: W = Fscos(theta), variable: W = integral Fdx KE: \frac{1}{2}$$mv^2 = p^$\frac{2}{2m}$ WET: $W_{net}$ = $delta_{KE}$ Gravity PE: mgh | Spring PE: \frac{1}{2}$$kx^2 Conservation: $KE_1$ + $PE_1$ = $KE_2$ + $PE_2$ (conservative only) With friction: $KE_1$ + $PE_1$ - f*d = $KE_2$ + $PE_2$ Power: P = Fv, $P_{avg}$ = $\frac{W}{t}$, 1 HP = 746 W Constant power: \frac{1}{2}$$mv^2 = Pt, v = sqrt$\frac{2Pt}{m}$ Terminal velocity: $v_{max}$ = $\frac{P}{f}$

Collisions (1D, $m_2$ at rest, elastic): $v_1$ = (m_{1-m}_2)$\frac{u_1}{m_1+m_2}$ $v_2$ = 2$m_1$*$\frac{u_1}{m_1+m_2}$

Inelastic: v = $m_1$*$\frac{u_1}{m_1+m_2}$, KE lost = $\frac{1}{2}$mu$u^2$

Restitution: e = sqrt(h'/h) for bouncing

Vertical circle: v_{bottom}_{min} = sqrt(5gR), v_{top}_{min} = sqrt(gR)