Rigid Body

A rigid body is a form of an ideal example where the body is subjected to no deformities at all. Also, it cannot change its shape or size. One more property of a rigid body is that if two mass particles exist in a closed system, the distance between them remains unchanged during their motion. 

So it can be concluded that the rigid body consisting of a single particle can never stand true. So all bodies are subjected to changing their shape or form when in motion. However, the change should be so small that it can be neglected. 

For example, there is a bridge. It won’t subject itself to change when a single man stands on it. But it will be subjected to change under the weight of a train. The change will be small so it is of no concern.

Rigid Body Dynamics

We have discussed the motion of rigid bodies in a plane in the following. Since the rigid body is considered a group of particles, determining its motion can seem like a huge task. Moreover, ignoring the fact that rigid bodies do not deform is a big risk at hand. So that is why the motion of every particle in the system is of utmost importance. It makes the dynamics of the kinematics involved trivial.

The Rigid Body is seen it have two kinds of motion –

1. Translational motion

2. Rotational motion

Translational Motion 

In this kind of motion, the body travels from one place to another in a straight line with no other forms of motion like rotation or anything. For Example, a bullet is fired from a gun.

Suppose the object is moving in a direction. If all the object particles move parallel, the motion is known as pure translational motion.

In this kind of motion, it is seen that all the particles of the object have the same velocity and acceleration in the same magnitude in the same direction at any given point of time. 

It is of two types –

1. Rectilinear motion – A bullet is fired from a gun

2. Curvilinear motion – Projectile motion with a trajectory

Rotational Motion

This kind of motion can be defined as the motion of an object when it rotates circularly in an unchanging orbit and a constant or fixed axis—for example, a rotating ceiling fan.

Also, it is seen that the object can be rotating along with its linear motion. For example, when a football is kicked on the ground, it is seen that the ball is rotating while moving in a straight line.

Since rotational motion is circular, physicists use radians or degrees for its study rather than metres to describe the displacement.

It is interesting to note that rotational motion is much more complex than linear motion due to the involvement of angles. It has its axis, a moment of inertia, the principle of conservation of angular momentum, which technically acts opposite to the conservation of linear momentum and centripetal force.

Centripetal force – The force which pushes an object to take a circular path is called centripetal force.

The differences in the formula of Translational and Rotational motion are described below –

Centre of Mass (COM)

It is indeed a special location assuming the object’s mass in reference is at a single place. For example, when you hang a ball on a string, the centre of mass will be below the support. 

Centres of Mass lie on a plane in symmetry. Highly symmetric bodies like a cube have their centre of mass literally at their centre. 

To find out about the centre of mass of a complex object, you must note each mass’s mean average weighted locations. For a group of masses, it will be,

(At three dimensions)

mi = masses

X,y,z = positions of the centres of masses.

Centre of Gravity

The Centre of Gravity in physics is thought to be the centre of mass of the body for the convenience of theoretical problems regarding the study of the object. It is particularly of great significance since it helps us to study objects when they are subjected to gravitational force.

Under a uniform gravitational field, sometimes the centre of mass and the centre of gravity collide. But this is not always the case. For example, if the object in reference is not made up of homogenous materials. So the centre of mass and gravity are bound to change.

Conclusion

Thus, a rigid body is a system of particles that are distanced equally, and the distance cannot be changed. Of course, in the real world, we do not have any perfectly rigid bodies as all bodies change by an external force, but in some cases, the change is so negligible that it is considered a rigid body. Some examples are earth, metal balls, etc.

Reaching equilibrium in rigid bodies requires more than one force acting in the opposite direction to reach a state where the body does not experience linear and angular momentum. When the body is in equilibrium, the vector sum of forces or torques is zero, and the linear and angular momentum does not change at a given point in time.

Thus we can say that the centre of gravity is of great significance in physics since it is thoroughly used for engineering purposes to construct buildings and such. 

In physics, there is a big focus on maths, for that matter.