Rigid Bodies

When an external force acts on a body and the distance between the two points on the body doesn’t change, then the body is known as a Rigid Body.

Or it can be said that a body that does not change shape under the influence of forces is known as a Rigid Body.

But practically there will be some forces under which the body will change shape. For example, a bridge will not change shape under the weight of a single person, but it might change shape under the weight of a truck, even though the change will be small.

As in real life, no substance is rigid; there is another concept regarding the body known as the resistant body, which is utilized in finding solutions for engineering problems.

To solve a range of problems that could not be explained with classical Physics, the Rigid Body and Rigid Body dynamics concept was developed. Motions like the potter wheel, rotation of the fan, etc. cannot be explained with a point mass. In a practical world, the deformation of wheel and steel rods is considered to be negligible and is considered as rigid.

Rigid Body Dynamics

What kind of motion could a Rigid Body have? This gave a new outlook, which meant that there could be two different types of Rigid Body motion. To have a better understanding of the world around us, we need to explore and understand different kinds of problems. What has come after Quantum Mechanism? The foundation of it is laid by the Rigid Body dynamics. The two types of motion that a Rigid Body undergoes are:

• Translational Motion

• Rotational Motion

What is a Translatory Motion?

Translational Motion definition– The motion with the help of which a body moves from one point in space to another is known as the Translational Motion. A typical example of Translatory motion is the motion of a bullet fired from a gun.

When the movement of a body is along a straight line, it is known as the rectilinear motion. In the following figure, a position occupied by the body at any time t is represented. With an appropriate sign, the distance x defines the position of the object. The motion of the object will be known when the position of the object at a particular time is known. This is expressed in the form of an equation that relates distance x, to time t. For example, x = 6t-4 or a graph. 

In two or three dimensions, the motion of an object is complicated. To fix the position of the object in the two dimensions, we need two coordinates.

Translational Motion Examples

The figure below shows Translational Motion examples or the simple example of projectile motion: a ball rolling off a table. The x-axis will define the horizontal direction, and the y-axis will determine the vertical direction. Considering the initial velocity of 10 m/s at which the ball is initially rolling on a flat table.

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When the ball is on the table the initial x-element of velocity (v_0x) is considered 10 m/s (constant), the initial y-element of velocity is 0 m/s, the x-component of acceleration is 0 m/s² and the y – element of acceleration is 0 m/s². The elements of velocity and acceleration are those parts of the velocity/acceleration that indicate the points in the x/y-direction.

Some other examples of Translational Motion are:

1. Moving the Bus

2. Sailing of Boat 

3. Dog Walking of Dog

4. A plant is shaken by a person

5. A stone falling straight at the surface of the earth

6. A coin moving over a carrom board

Rotational Motion Physics

Rotational Motion is a common type of circular motion. Similar to projectile motion, the kinematics can be analyzed, and the relationships between the position, acceleration, and velocity can be learned. As per Newton's first law, an object in motion remains in motion at a constant velocity unless an external force acts upon it. If the force applied is perpendicular to the direction of motion, there will be a change in the direction of the velocity. The object will move at a constant speed in a circular path if a force continuously acts perpendicular to the moving object; this is known as uniform circular motion.

Rotational Motion Physics deals only with Rigid Bodies. A body that retains its overall shape is known as the Rigid Body, meaning the particle that makes the body remain in a similar position relative to one another. 

Rotational Motion Examples

The common example of Rotational Motion of a Rigid Body is the wheel or the rotor of a motor, which appears in the questions involving rotation motion. 

For translator motion, some of the examples are: Man running.

Other examples:

1. Moving by Bus

2. Sailing of Boat

3. Dog walking

4. A person shaking the plant.

5. A stone falls straight at the surface of the earth.

6. Movement of a coin over a carrom board 

When every particle of a body moves in a circular path around a line, it is called the axis of rotation. The circular motion of the Rigid Body occurs, and it cuts through the center of the mass. This is shown in the diagram below.

Rigid Bodies

A Rigid Body is generally defined as a body on which the distance between two points never changes whatever be the force applied on it. Or in other words, it can be said that the body which does not deform under the influence of forces is known as a Rigid Body. But, in real-life scenarios, there would be some force under which the body starts to deform. A Rigid Body is a type of body that does not deform or vibrate. As opposed to Rigid Bodies, Continuum mechanics deals with deformable bodies. A Rigid Body is one where every atom is always in the same position concerning every other atom in the body and even when outside forces are applied to the body. An example of a Rigid Body is like, a bridge that does not deform under the weight of a single man but it may deform under a load of a truck or ten trucks but the deformation is small.

Properties of Rigid Body Motion

There are two properties of the motion of Rigid Bodies that simplify the kinematics significantly. To identify this, it is observed that an arbitrary Rigid Body motion falls into one of the three categories: Translational Motion, Rotational Motion, and General Plane Motion.

Translation, curvilinear, and rectilinear: Translational Motion is the type of motion in which every line in the body remains parallel to its original position. In Translational Motion, the motion of the body is completely specified by the motion of any point in the body and All points of the body have the same velocity and same acceleration.

Some examples of Translational Motion are:

• Moving the Bus

• Sailing of Boat 

• Dog Walking of Dog

• A plant is shaken by a person

• A coin moving over a carrom board

Rotational Motion: Rotational Motion is a type of motion that has a Rotation about a fixed axis. All particles in Rotational Motion move in circular paths about the axis of rotation. The Rotational Motion of the body is completely determined by the angular velocity of the rotation.

Some examples of Rotational Motion are:

• Moving by Bus

• Sailing of Boat

• Dog walking

• A person shaking the plant.

• Movement of a coin over a carrom board 

General Plane Motion: General plane motion is a type of motion that is defined as Any plane motion that is neither a pure rotation nor a translation falls into this class. However, a general plane motion can always be reduced to the sum of a translation and a rotation.

Examples of Rigid Bodies

One general real-time example of a Rigid Body is a ball bearing made of hardened steel is a good example of a Rigid Body. Now, try to drop a ball bearing on a polished marble floor it will bounce just about as well as a Superball. Why is that? It is because, though it is a Rigid Body, it has near-perfect elasticity. So, no matter how rigid a body is, it still has quantum fields that are electromagnetic forces between atoms. So basically, in a very hard object, almost no mechanical energy is lost if someone taps it because it is like a perfect spring, albeit extremely hard. And, if you heat it, it will expand slightly. Again, it will happen also because of the atomic forces acting between the neighboring atoms. When the body is heated, they vibrate faster, creating expansion. Now, the total opposite of such a Rigid Body would be a lump of silly putty or dough. If someone throws it with full force at the wall, it will just stick, and either ooze or drop down the wall. All the force of the impact that is applied to that body went into inelastic mechanical deformation.

Now the second example would be, the flutter of an aircraft wing during the course of a flight is clearly negligible relative to the motion of the aircraft as a whole. On the other hand, if someone was interested in stresses induced in the wing as a consequence of the flutter, these deformations become of primary importance.