---
title: "Principles of mechanics; perfectly rigid assumption"
subject: "Applied Mechanics"
chapter: 1
key: "semester_1/applied_mechanics:principles-applied-mechanics-perfectly-rigid"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/principles-applied-mechanics-perfectly-rigid
site: BCT Engineering
---

# Principles of mechanics; perfectly rigid assumption

Applied Mechanics · Chapter 1: Introduction

- Asked in: 2071 Chaitra, 3+3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/principles-applied-mechanics-perfectly-rigid
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-1

## Question

Explain about the principles of Applied Mechanics. Why is it necessary to assume a solid body as 'perfectly rigid' for the study of statics?

## Short answer

The principles include Newton’s laws, the law of gravitation, the parallelogram law, and the principle of transmissibility. A solid body is assumed perfectly rigid in statics because real deformations are too small to affect geometry, so equilibrium equations can be applied to the original dimensions, transmissibility holds, and analysis is simpler.

## Answer

#### Principles of applied mechanics
- **Newton's first law:** a body continues in its state of rest or of uniform straight-line motion unless an external force compels it to change.
- **Newton's second law:** the acceleration produced is directly proportional to the resultant force and in the same direction, so F = ma.
- **Newton's third law:** for every action there is an equal and opposite reaction. Forces between two bodies in contact are equal, opposite and collinear.
- **Law of gravitation:** two particles of masses m₁ and m₂ at distance r attract each other with F = G m₁m₂/r². The weight of a body is W = mg.
- **Parallelogram law:** the resultant R of two forces P and Q acting at a point is given in magnitude and direction by the diagonal of the parallelogram, R = √(P² + Q² + 2PQ cos α).
- **Principle of transmissibility:** a force may be moved anywhere along its line of action without changing its external effect on a rigid body.

#### Why a solid body is taken as perfectly rigid in statics
- Real solids deform only slightly under load, so the shape and dimensions can be taken as unchanged. The moment arms and angles then stay as in the original geometry.
- The equilibrium equations can be applied directly to the undeformed body, which makes the analysis simple.
- Transmissibility is valid only for rigid bodies.
- The small error is acceptable, because the purpose of statics is to find the external forces and support reactions. The deformation itself is studied in strength of materials.

## Check yourself

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

1. The magnitude of the resultant of P and Q with angle alpha between them is:
   A. sqrt(P^2 + Q^2 - 2PQ cos alpha)
   B. sqrt(P^2 + Q^2 + 2PQ cos alpha)
   C. P + Q always
   D. (P^2 + Q^2) cos alpha
   Answer: B. The parallelogram law gives R = sqrt(P^2 + Q^2 + 2PQ cos alpha). (Key point: Parallelogram law)

2. The principle of transmissibility is valid for:
   A. A cable only
   B. A fluid only
   C. Only a rigid body
   D. Any deformable body
   Answer: C. Transmissibility is valid only for rigid bodies. (Key point: Transmissibility)

3. Why is a solid taken as perfectly rigid in statics?
   A. So that moment arms and angles stay as in the original geometry and equilibrium can be applied directly
   B. Because forces then vanish
   C. Because real solids never deform
   D. Because strength of materials is not needed for any problem
   Answer: A. The small deformation is neglected, so equilibrium is applied to the undeformed body. (Key point: Why rigid in statics)

4. The weight of a body of mass m is:
   A. W = G m
   B. W = m/g
   C. W = mg^2
   D. W = mg
   Answer: D. Weight is mass times gravitational acceleration, W = mg. (Key point: Weight)

## Related in Applied Mechanics

- [Rigid body and perfectly rigid assumption](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Arigid-body-perfectly-rigid-assumption) — Applied Mechanics, chapter 1, 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
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- [Scope and importance of applied mechanics; FBD](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Ascope-importance-applied-mechanics-fbd) — 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×
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