16.8: Equation of Motion for a Rigid Body
The movement of a rigid object can be understood through the equations that explain both translational and rotational motion about the center of mass of the object, point G. This center of mass is the point where the equation of motion for translational motion comes into play, as per Newton's Second Law.
The combined moments generated about the center of mass of the object are equal to the rate of change of the angular momentum of the body. An external force, when applied at a different point other than the center of mass of the object, causes the body to rotate and generates a moment.
The angular momentum of this point is articulated as a vector product, incorporating its relative position and velocity with respect to the center of mass of the object. The derivative of angular momentum with respect to time provides us with the moment generated at a point where an external force is applied. By summing the moments of all points within the rigid body, one can calculate the total moment of the system about the center of mass of the object.
