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: (2/5)MR^2; Hollow sphere: (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 = (1/2)Mv^2(1 + k^2/R^2)
• Incline acceleration: a = g*sin(theta)/(1 + k^2/R^2)

Energy fractions (solid sphere):

• KE_trans/KE_total = 5/7, KE_rot/KE_total = 2/7