Question

In non-uniform circular motion, the ratio of tangential to radial acceleration is (r =radius of a circle, v = speed of the particle, $\alpha$ = angular acceleration)

• A. $\frac{{\alpha }^2{r}^2}{v}$
• B. $\frac{{\alpha }^{2}r}{v^2}$
• C. $\frac{\alpha r^2}{v^2}$
• D. $\frac{v^2}{r^2\alpha }$

Answer 1

Answer: (C)

$\frac{\alpha r^2}{v^2}$

Tangential acceleration, $a_t=\alpha .r$ where $\alpha$=angular acceleration and $r$=radius

Radial acceleration,$a_r=\frac{v^2}{r}$ where $v$=speed of particle

Hence, $\frac{a_t}{a_r}=\frac{\alpha .r^2}{v^2}$

Hence, answer is option-(C).