Key Equations

Key Equations

Velocity of center of mass of rolling object	$v_{\text{CM}}=R\omega$
Acceleration of center of mass of rolling object	$a_{\text{CM}}=R\alpha$
Displacement of center of mass of rolling object	$d_{\text{CM}}=R\theta$
Acceleration of an object rolling without slipping	$a_{\text{CM}}=\frac{mg\text{sin}\theta }{m+(I_{\text{CM}}\text{/}{r}^2)}$
Angular momentum	$\overrightarrow{l}=\overrightarrow{r}\times \overrightarrow{p}$
Derivative of angular momentum equals torque	$\frac{d\overrightarrow{l}}{dt}={\displaystyle \sum \overrightarrow{\tau }}$
Angular momentum of a system of particles	$\overrightarrow{L}={\overrightarrow{l}}_1+{\overrightarrow{l}}_2+\cdots +{\overrightarrow{l}}_N$
For a system of particles, derivative of angular momentum equals torque	$\frac{d\overrightarrow{L}}{dt}={\displaystyle \sum \overrightarrow{\tau }}$
Angular momentum of a rotating rigid body	$L=I\omega$
Conservation of angular momentum	$\frac{d\overrightarrow{L}}{dt}=0$
Conservation of angular momentum	$\overrightarrow{L}={\overrightarrow{l}}_1+{\overrightarrow{l}}_2+\cdots +{\overrightarrow{l}}_N=\text{constant}$
Precessional angular velocity	${\omega }_P=\frac{rMg}{I\omega }$