Question

If a particle is rotating in a circle of radius R with velocity at an instant v and the tangential acceleration is a. Find the net acceleration of the particle.

Answer 1

\(\vec a_{\text{net}}= \vec a_{\text{radial}} +\vec a _{\text{tangential}}\)

\(\vec a_r = \frac {v^2}R. (- \hat e_r); \)

\(\vec a_t = a(\hat e_t)\)

\(|\vec a_{net}| = \sqrt{a^2 + \left(\frac {v^2}R\right)} m/s^2\)

Answer 2

Answer is given as

\(\sqrt{a^2 + (\frac{v^2}{R})^2}\)