Module 1 : Dynamics of Rigid Bodies in Plane Motion; Dynamic Force Analysis of Machines
Lecture 1 : Dynamics of Rigid Bodies in Plane Motion; Dynamic Force Analysis of Machines.
Adding up the equations of all the elemental masses (keeping in mind that the internal reaction forces occur in equal but opposite pairs), we get the equations of motion for the body, relating linear accelerations to linear forces
(2)
Where a c is the acceleration of the centre of mass. Note that the force and acceleration vectors, though three dimensional, lie in the plane of motion of the rigid body. Hence, resolving the forces along the x and y directions in the plane, we get two scalar equations of motion.
(3)
The third equation in planar motion, for the rotation of the body is obtained as:
(4)
where Ic , the moment of inertia about the center of mass is given by
(5)
Equations (3) and (4) are the fundamental equations of motion of a rigid body in planar motion.
