Key Equations

Velocity of center of mass of rolling object	$v_{CM} = R ω$
Acceleration of center of mass of rolling object	$a_{CM} = R α$
Displacement of center of mass of rolling object	$d_{CM} = R θ$
Acceleration of an object rolling without slipping	$a_{CM} = \frac{m g sin θ}{m + (I_{CM} / r^{2})}$
Angular momentum	$\vec{l} = \vec{r} \times \vec{p}$
Derivative of angular momentum equals torque	$\frac{d \vec{l}}{d t} = \sum \vec{τ}$
Angular momentum of a system of particles	$\vec{L} = {\vec{l}}_{1} + {\vec{l}}_{2} + \dots + {\vec{l}}_{N}$
For a system of particles, derivative of angular momentum equals torque	$\frac{d \vec{L}}{d t} = \sum \vec{τ}$
Angular momentum of a rotating rigid body	$L = I ω$
Conservation of angular momentum	$\frac{d \vec{L}}{d t} = 0$
Conservation of angular momentum	$\vec{L} = {\vec{l}}_{1} + {\vec{l}}_{2} + \dots + {\vec{l}}_{N} = constant$
Precessional angular velocity	$ω_{P} = \frac{r M g}{I ω}$