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Mechanical Engineering QUESTION #2516
Question 1
In normal-tangential (n-t) coordinates, the acceleration of a particle moving along a curved path with speed \(v\) and radius of curvature \(\rho\) is:
  • Only the tangential component \(\dot{v}\,\hat{e}_t\)
  • Only the normal component \(\frac{v^2}{\rho}\hat{e}_n\)
  • Both \(a_t = \dot{v}\) tangentially and \(a_n = \frac{v^2}{\rho}\) normally✔️
  • A single vector directed toward the center of curvature
Correct Answer Explanation
In n-t coordinates: \(\mathbf{a}=\dot{v}\hat{e}_t + \frac{v^2}{\rho}\hat{e}_n\). The tangential component \(a_t=\dot{v}\) reflects speed change; the normal (centripetal) component \(a_n=v^2/\rho\) reflects direction change.