In mechanics, one often uses the model of a perfectly rigid...

Name: Problem 15, Chapter 35: University Physics with Modern Physics
Uploaded: 2021-08-05T11:15:26-08:00
Duration: 52 s
Channel: Bettina Hanlon
Description: In mechanics, one often uses the model of a perfectly rigid body to determine the motion of physical objects (see, for example, Chapter 10 on rotation). Explain how this model contradicts Einstein's special theory of relativity.

In mechanics, one often uses the model of a perfectly rigid body to determine the motion of physical objects (see, for example, Chapter 10 on rotation). Explain how this model contradicts Einstein's special theory of relativity.

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Key Concepts

Special Theory of Relativity

Einstein’s special theory of relativity establishes that no information or physical effect can travel faster than the speed of light. This limitation means that any change, such as a force or deformation, must propagate at a finite speed, contradicting the notion of instantaneous effects throughout a rigid body.

Propagation of Forces

In reality, forces and deformations propagate at finite speeds (for example, as stress waves in materials), ensuring that no part of an object can respond before the effect has had time to reach it. This concept directly conflicts with the rigid body assumption, highlighting the incompatibility between classical rigidity and relativistic constraints.

Rigid Body Model

In classical mechanics, a perfectly rigid body is assumed to deform not at all under the influence of forces, meaning that any applied force causes an instantaneous acceleration across the entire object. This assumption simplifies analysis in many mechanical problems but inherently relies on the idea of instant propagation of internal forces.

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