Question

A particle is moving under a central force along the path given by the equation r = a tan \theta.Show that the radial acceleration is \frac{k^2}{r^2}\left \{ 3 + \frac{2a^2}{r^2} \right \} where, k = r^2\frac{d\theta }{dt} .

15 Feb 2018
Answer :
Word Count : 380
To solve the problem of finding the radial acceleration of a particle moving under a central force along the path \( r = a \tan \theta \), where the given condition for \( k \) is \( k = r^2 \frac{d\theta}{dt} \), we can break it down step by step. ### Step 1: Radial acceleration formula The radial acceleration \( a_r \) in polar coordinates is given by: \[ a_r = \ddot{r} - r \dot{\theta}^2 \] Where: - \( r \) is the radial distance, - \( \dot{r} \) is the rate of change of
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