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Key Equations

Velocity of center of mass of rolling object vCM=RωvCM=Rω
Acceleration of center of mass of rolling object aCM=RαaCM=Rα
Displacement of center of mass of rolling object dCM=RθdCM=Rθ
Acceleration of an object rolling without slipping aCM=mgsinθm+(ICM/r2)aCM=mgsinθm+(ICM/r2)
Angular momentum l=r×pl=r×p
Derivative of angular momentum equals torque dldt=τdldt=τ
Angular momentum of a system of particles L=l1+l2++lNL=l1+l2++lN
For a system of particles, derivative of angular
momentum equals torque
dLdt=τdLdt=τ
Angular momentum of a rotating rigid body L=IωL=Iω
Conservation of angular momentum dLdt=0dLdt=0
Conservation of angular momentum L=l1+l2++lN=constantL=l1+l2++lN=constant
Precessional angular velocity ωP=rMgIωωP=rMgIω
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