Kinetics of Rigid Bodies: Force and Acceleration

Kinetics of Rigid Bodies: Force and Acceleration

This topic extends Newton's Second Law to rigid bodies, relating forces and torques to linear and angular acceleration.

Equations of Motion

For a rigid body in plane motion:

$\sum F_x = m (a_G)_x$ $\sum F_y = m (a_G)_y$ $\sum M_G = I_G \alpha$

Where:

• $G$ is the center of mass.
• $I_G$ is the mass moment of inertia about $G$.
• $\alpha$ is the angular acceleration.

Rotation about a Fixed Axis

For rotation about a fixed point $O$: $\sum M_O = I_O \alpha$ Where $I_O = I_G + m d^2$ (Parallel Axis Theorem).

Example: Unbalanced Wheel