Equations for Plane Motion

For rigid bodies, we will describe the previous quantities such that

• R is the resultant of the forces acting on the rigid body at a given instant of time
• m is the mass of the rigid body
• a_G is the instantaneous linear acceleration of the mass center of the rigid body in the direction of the resultant force R

The actual motion of most rigid bodies consists of the superposition of a translation produced by R and a rotation produced by the moment of R when its line of action does not pass through the mass center G of the body.

The text goes through a careful derivation of the moments about point A caused by internal and external forces f and F, respectively. In short, the derivation arrives at

where I represents the moment of inertia of the rigid body.

Depending on the type of problem, we will generally be able to simplify these relationships.

• If the body is symmetric about the plane of motion,

• If the body is symmetric about the plane of motion and the acceleration of point A is zero (fixed axis rotation),

• If the body is symmetric about the plane of motion and point A coincides with G,