---
title: "Rigid body and perfectly rigid assumption"
subject: "Applied Mechanics"
chapter: 1
key: "semester_1/applied_mechanics:rigid-body-perfectly-rigid-assumption"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/rigid-body-perfectly-rigid-assumption
site: BCT Engineering
---

# Rigid body and perfectly rigid assumption

Applied Mechanics · Chapter 1: Introduction

- Asked in: 2073 Shrawan, 3 marks; 2071 Shrawan, 3 marks (asked 2 times)
- Video: [Why Engineers Pretend a Car Is Just a Dot | Particle vs Rigid Body | Tech And Engineering](https://www.youtube.com/watch?v=TxhtMV_M_eM) — Tech And Engineering 
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/rigid-body-perfectly-rigid-assumption
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-1

## Question

What do you understand by a Rigid Body? Why is it necessary to assume a body as 'perfectly rigid' for your present study?

## Short answer

A rigid body is an idealized body in which the distance between any two points remains constant under loading, so it does not deform. It is assumed perfectly rigid in statics because real deformations are negligible, allowing equilibrium equations to be applied to the original geometry and the principle of transmissibility to be used, greatly simplifying analysis.

## Answer

#### Rigid body
A rigid body is an idealised body in which the distance between any two particles always remains constant, however large the forces acting on it are. It does not change its shape or size under load, so there is no deformation.

#### Why 'perfectly rigid' is assumed
- Every real body deforms a little under load. In statics the deformations are very small compared with the size of the body, so the geometry (the lengths and angles that fix the lines of action and moment arms) is practically unchanged.
- With this assumption the equations of equilibrium (ΣF = 0, ΣM = 0) can be written using the original, undeformed dimensions. There is no need to know how the body deforms.
- The principle of transmissibility holds only for a rigid body. A force can then be slid along its line of action, which makes finding resultants and moments simple.
- Material properties such as the modulus of elasticity are not needed, so the problem reduces to pure geometry and force balance.
- Deformation and stress are studied separately in strength of materials, where the body is treated as deformable.

So the assumption simplifies the analysis a great deal, while the error it introduces is negligible for the bodies met in statics.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. A rigid body is one in which:
   A. The distance between any two particles stays constant however large the force
   B. The body stretches slightly but returns to shape
   C. Only the mass is considered, not the size
   D. The distance between particles increases with load
   Answer: A. There is no change of shape or size, so no deformation. (Key point: Rigid body)

2. Why can equilibrium equations be written using the original dimensions in statics?
   A. Moments are always zero for solids
   B. Deformations are very small, so lengths, angles and moment arms are practically unchanged
   C. The modulus of elasticity is always large
   D. Real bodies do not deform at all
   Answer: B. Small deformations leave the geometry practically unchanged, so no deformation analysis is needed. (Key point: Why assume rigid)

3. Which principle holds only for a rigid body?
   A. Law of gravitation
   B. Principle of transmissibility
   C. Newton's third law
   D. Parallelogram law
   Answer: B. A force can be slid along its line of action only if the body is rigid. (Key point: Transmissibility)

## Related in Applied Mechanics

- [Principles of mechanics; perfectly rigid assumption](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aprinciples-applied-mechanics-perfectly-rigid) — Applied Mechanics, chapter 1
- [Rigid vs deformable bodies; free body diagram](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Arigid-deformable-bodies-fbd) — Applied Mechanics, chapter 2, asked 2×
- [Fundamental principles of applied mechanics; rigid body](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Afundamental-principles-define-rigid-body) — Applied Mechanics, chapter 1
- [Concept of particle, rigid and deformable body](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aconcept-particle-rigid-deformable) — Applied Mechanics, chapter 1
- [Rigid and deformable body; FBD principles](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Arigid-deformable-fbd-principles-static-equilibrium) — Applied Mechanics, chapter 2

## Related in other subjects

- [Rigid body motion types; double gear velocities](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Adouble-gear-rack-velocity-types-motion) — Applied Mechanics (Dynamics), chapter 4
- [Angular momentum of rigid body in plane motion](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Aangular-momentum-rigid-body-plane) — Applied Mechanics (Dynamics), chapter 5
- [Kinetic energy and work of rigid body](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_mechanics%3Akinetic-energy-rigid-body-work-energy) — Engineering Mechanics, chapter 7