We can use Newton 's equations for particles to derive the equations of motion of a rigid body. A rigid body, which is constrained to move in a plane, has three degrees of freedom, and hence it has three independent equations of motion which relate the forces in the plane to accelerations. Consider the body shown in Fig. 1.1 (a). A set of forces  and couples  act on it, with the force  acting at the point  . The position coordinates are with respect to an inertial frame. The rigid body can be considered to be made of elemental masses which can be regarded as particles. Newton 's equation for the  elemental mass  (Fig. 1.1 (b)) at the location  is |
is the external force acting on it. Note that every elemental mass may not have an external force. 
is the force on the 
elemental mass from the 
elemental mass. This arises due to the constraint that the two masses have to remain at a fixed distance from each other. 
