University Physics Volume 1

Key Equations

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 $l→=r→×p→l→=r→×p→$ Derivative of angular momentum equals torque $dl→dt=∑τ→dl→dt=∑τ→$ Angular momentum of a system of particles $L→=l→1+l→2+⋯+l→NL→=l→1+l→2+⋯+l→N$ For a system of particles, derivative of angularmomentum equals torque $dL→dt=∑τ→dL→dt=∑τ→$ Angular momentum of a rotating rigid body $L=IωL=Iω$ Conservation of angular momentum $dL→dt=0dL→dt=0$ Conservation of angular momentum $L→=l→1+l→2+⋯+l→N=constantL→=l→1+l→2+⋯+l→N=constant$ Precessional angular velocity $ωP=rMgIωωP=rMgIω$