Motion of the System of Particles and Rigid Body Definition Formula Example

Motion of the System of Particles and Rigid Body: Candidates looking for the system’s motion and other particle information must check the detailed information for candidate reference purposes. A rigid body is nothing but an object with a perfectly defined shape that is unchangeable. However, most real bodies deform under the influence of forces. Euler’s angle and Euler’s equations should be introduced to describe a rigid body’s attitude and its evolution. Students also recall the transformation matrix between different reference frames.

For Motion of the System of Particles and Rigid Body, with classical physics, rigid body dynamics are concepts developed to explain the motions of a fan, a potter’s wheel, a top, etc.

What is a System of Particles

A cell system is a group of cells that are related to each other. The equations of the System of particles are easily used to develop them for a rigid body. A new but essential concept introduced to the System of particles is the center of mass.

But in mechanics, a system of particles is a collection of more than one specified particle.

Consider a rectangular block sliding down an inclined surface without lateral motion. It is a rigid body, and its movement in a plane is such that all body parts move together. All particles will have the same velocity at any time. Thus, this rigid body is in pure translational motion here. At any instant, in pure translational motion, it can be concluded that all particles in the body will have the same velocity.

Solid metallic or wooden cylinder

Here, for example, we take the rolling motion of a solid metal/wooden cylinder down a similar inclined plane discussed above. The cylinder is a rigid body that moves from top to bottom of an inclined plane and thus exhibits translational motion. But here, all the cells in this body do not move at the same speed at any moment.

Thus, the cylindrical body is not in the pure translation. There is another addition to translational motion.

By constraining a rigid body, it has no translational motion. So, we can fix it along a straight line (axis of rotation). The only type of motion it can exhibit is rotation.

Rotation of System of particles and rigid body

When a body is about a fixed axis, everybody particle moves in a circular motion and lies in one plane perpendicular to an axis having its center on the axis. It is called rotation.

Center of Mass of System of particles and rigid body

After some experiments, it was established that the center of mass of a system of particles is moving, the entire System’s mass is concentrated at its center, and all external forces are applied at the central point. Also, it is known that the total momentum of a system of particles is equal to the body’s total mass or System and the velocity of its center of mass.

The center of mass can be described as the average position of all the system components or the average position of the mass distribution in space. It is the point where a force is applied that results in a linear acceleration without any angular acceleration. The motions of this point are equal to the motion of a single particle, and the mass of this particle is equal to the sum of all the individual particles in the System through the action of the surrounding bodies or the force field directly applied to that particle.

Conclusion

The motion of particles and systems of rigid bodies includes concepts such as the center of mass, torque, angular momentum, conservation of angular momentum, the radius of gyration, and theorems about vertical and horizontal axes.