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Mechanical Engineering QUESTION #2517
Question 1
A particle of mass \(m\) moves under a central force. By Newton's second law in polar coordinates \((r,\theta)\), the radial equation of motion is:
  • \(F_r = m(\ddot{r} + r\dot{\theta}^2)\)
  • \(F_r = m(\ddot{r} - r\dot{\theta}^2)\)✔️
  • \(F_r = m\,r\ddot{\theta}\)
  • \(F_r = m(\dot{r}\dot{\theta} + r\ddot{\theta})\)
Correct Answer Explanation
In polar coordinates, the radial acceleration is \(a_r=\ddot{r}-r\dot{\theta}^2\). Newton's law gives \(F_r=m(\ddot{r}-r\dot{\theta}^2)\).