 # Rigid Bodies

### What is a Rigid Body?

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 are considered to be negligible and are 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 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.

When the ball is on the table the initial x-element of velocity (v0x) 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 of Bus

2. Sailing of Boat

3. 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 the 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.

The 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 falling 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 centre of the mass. This is shown in the diagram below.

1. Is Vibratory Motion an Example of Translatory Motion?

Ans In all states like liquid, solid, and gas, the particles of the matter have vibratory motions. In liquid and gas, there are also rotary and translatory motions.

In solid only vibratory motion occurs, which is due to the vibration between the two molecules. Since there is a tiny distance between the molecules of a solid, it is fast and efficient in transmission of vibration.

As translatory motion is not possible in solid; one can answer the question as to why we cannot use them at pistons contrary to the gases and the liquids.

By looking at solids like the spring, you might think that translator motion is possible, but it is due to the vibration and its flexibility. Due to the flexibility, it allows vibration to occur most easily. As the vibration spreads, it mobilizes the solid.

2. Translational Motion Versus Rotational Motion.

Ans There is a strong correlation between standard translational motion and rotational motion. Indeed, each physical theory used to scrutinize rotational motion has its translational concurrent. (table will be uploaded soon)