Question

Find the radial and angular components of acceleration for the motion TT r = 1 + cos e, = e-t at 0 2

Answer 1

The acceleration vector in polar co-ordinates is d = ( - rᎾ )f + ( Ꮎ + 2rᎾ Ꮎ is radial component of acceleration vector. is angular component of acceleration vector.

Given T = 1 + cose A= -t       $\Rightarrow \dot{r}=\theta sin(\theta )$ $\ddot{r}=\frac{d\dot{r}}{dt}=\frac{d\dot{r}}{d\theta }\frac{d\theta }{dt}$ $\therefore \ddot{r}=(\theta cos(\theta )+sin(\theta ))(-e^{-t})$ :.j = (cos(O) + sin(O)(-)

  

Radial component of acceleration $a_{r}=-\theta ^{2} cos(\theta )-\theta sin(\theta )-(1+cos(\theta ))(-\theta )^{2}$    at  $\theta =\frac{\pi }{2}$

Angular component of acceleration $a_{\theta }=\theta +cos(\theta )\theta -2sin(\theta )\theta ^{2}$ at  $\theta =\frac{\pi }{2}$