Rigid Body

Rigid Body

Have you ever tried breaking a twig in two? Or shattered glass when it accidentally slipped from your hand? Now imagine an object that, no matter how much you drop, twist, or strike, does not break. Imagine that it also never changes its shape under any condition. This object that you just imagined is a rigid body. And while there are no perfect examples of a rigid body, there are many solid bodies that are very close to rigid bodies. Let’s begin with the definition of a rigid body.

A rigid body is an ideal solid body that retains its shape under all conditions and never deforms. In a rigid body, deformation is considered nil or so small that it can be neglected while calculating. 

Properties of Rigid Body

• A rigid body can be seen as a collection of particles made into solid matter. In a rigid body, the distance between any two particles remains constant in time. It is unaffected by any external forces or moments exerted on the rigid body.

1. Consider a rigid body and two points of the rigid body are point j, and point k.
2. The distance between these two points remains constant, as per the laws of a rigid body and this distance is defined by rk.j
3. The distance value, although constant, can be positive or negative, depending on whether you calculate it from j to k or vice versa.
4. However, the magnitude of the distance between two points of the solid body, j and k, always remains the same.
5. The magnitude of distance can be represented as follows: 
6. | rk.j | ~ rk.j =  constant.

• A rigid body is idealised to have an equal mass distribution throughout its solid shape.
• In reality, all solid bodies deform as they move. However, if the body’s deformation is negligible compared to the overall motion of the body, it can be accepted as a rigid body. 

Properties of Rigid Body in Motion

• When a rigid body is in motion, every line in the body remains parallel to its original position.
• All points of the body have the same velocity and acceleration when a rigid body is in motion.
• If a rigid body is rotating about a fixed axis, every particle of the body moves in perfect circles around the axis of rotation. Therefore, you can determine the body’s motion in this case through the rotation’s angular velocity.

Examples of Rigid Body

In theory, a rigid body exists only in imagination. This is because no such object does not deform due to external factors, especially when it is in motion. However, there are practical usages of a rigid body. In the real world, a body that deforms only negligibly as compared to the motion it is going through is considered a rigid body.

Some examples of a rigid body are as follows:

• A ball bearing made of hardened steel is an example of a rigid body. A ball bearing loses almost no mechanical energy and retains its maximum shape upon bouncing or tapping. Thus, it is an example of a rigid body.
• Consider a bridge that is used for transport. While it consistently supports the tonnes of weight, it only undergoes slight deformation. It can hence be considered a rigid body.
• The third example of a rigid body is the wing of an aeroplane. During a flight, the motion experienced by this wing is negligible. Hence, its deformation is ignored.
• Quantum mechanics considers molecules or point masses as rigid bodies.

Conclusion

This chapter taught us the basic properties and examples of a rigid body. Also go through the frequently asked questions on the topic stated below. You can further understand the topic of a rigid body by learning about rigid bodies in motion and the kinetic energy of rigid bodies.