Kinetics of Rigid Bodies: Impulse and Momentum

Kinetics of Rigid Bodies: Impulse and Momentum

This method relates the forces and moments acting over time to the change in linear and angular momentum of the body.

Angular Momentum ($H$)

• About Center of Mass ($G$): $H_G = I_G \omega$
• About Fixed Point ($O$): $H_O = I_O \omega$

Principle of Impulse and Momentum

The system of momenta at time $t_1$ plus the system of impulses from $t_1$ to $t_2$ equals the system of momenta at $t_2$.

Linear Impulse-Momentum: $m(v_G)_1 + \sum \int F \, dt = m(v_G)_2$

Angular Impulse-Momentum (about $G$): $I_G \omega_1 + \sum \int M_G \, dt = I_G \omega_2$

Example: Spinning Disk