Moment of Inertia:

• Rod (centre): $ML^2$/12; (end): $ML^2$/3
• Ring (axis): $MR^2$; (diameter): $MR^2$/2
• Disc (axis): $MR^2$/2; (diameter): $MR^2$/4
• Solid sphere: \frac{2}{5}$$MR^2; Hollow sphere: \frac{2}{3}$$MR^2

Axis Theorems:

• Parallel: I = $I_{cm}$ + $Md^2$
• Perpendicular: $I_z$ = $I_x$ + $I_y$ (2D only)

Dynamics:

• tau = Ialpha, L = Iomega, P = tau*omega
• Angular impulse = Delta(L) = tau*Delta(t)

Rolling (no slip):

• v = Romega, a = Ralpha
• KE = \frac{1}{2}$$Mv^2(1 + $k^2$/$R^2$)
• Incline acceleration: a = g*sin$\frac{theta}{(1 + k^2/R^2)}$

Energy fractions (solid sphere):

• $KE_{trans}$/$KE_{total}$ = 5/7, $KE_{rot}$/$KE_{total}$ = 2/7