Chapter 10: Q8P (page 517)

Write the transformation equations for $W \times S$ to verify the results of Example 3.

Short Answer

Expert verified

This answer proves that $W \times S$ is a polar vector.

Step by step solution

Given information.

Matrix definitions are given.

Definition of transformation laws.

Define the transformation laws.

${W_{i}}^{'} = a_{i j} W_{j} {S_{i}}^{'} = (d e t A) a_{i j} S_{j}$

Define the transformation laws.

Write the transformation laws assuming and are axial and polar vectors.

${W_{i}}^{'} = a_{ij} W_{j} {S_{i}}^{'} = (d e t A) a_{i j} S_{j}$

Continue the evaluations.

Write the implication of the transformation laws.

${(W' \times S')}_{α} = ε'_{α β γ} W_{β}' S_{γ}' = (d e t A) a_{α i} a_{β j} a_{γ k} ε_{i j k} a_{β m} w_{m} (d e t A) a_{γ m} S_{n} = {(d e t A)}^{2} a_{c i} ε_{i j k} w j S_{k} = a_{α i} {(W \times S)}_{I_{}}$

This implies that $W \times S$ is a polar vector.

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Write the transformation equations for $W \times S$ to verify the results of Example 3.

Short Answer

Step by step solution

Given information.

Definition of transformation laws.

Define the transformation laws.

Continue the evaluations.

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Write the transformation equations forW×S to verify the results of Example 3.

Short Answer

Step by step solution

Given information.

Definition of transformation laws.

Define the transformation laws.

Continue the evaluations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Medical Physics

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Study anywhere. Anytime. Across all devices.

Write the transformation equations for $W \times S$ to verify the results of Example 3.