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Mechanical Engineering QUESTION #2524
Question 1
Poisson's relations for a rotating reference frame with angular velocity \(\boldsymbol{\omega}\) give the time derivatives of unit vectors \(\hat{i},\hat{j},\hat{k}\) as:
  • \(\dot{\hat{i}}=\hat{i}+\boldsymbol{\omega}\)
  • \(\dot{\hat{i}}=\boldsymbol{\omega}\times\hat{i}\)✔️
  • \(\dot{\hat{i}}=\boldsymbol{\omega}\cdot\hat{i}\)
  • \(\dot{\hat{i}}=\hat{i}/\omega\)
Correct Answer Explanation
Poisson's relations state that the time derivatives of the rotating unit vectors are: \(\dot{\hat{i}}=\boldsymbol{\omega}\times\hat{i}\), \(\dot{\hat{j}}=\boldsymbol{\omega}\times\hat{j}\), \(\dot{\hat{k}}=\boldsymbol{\omega}\times\hat{k}\).