$A$ particle moves along a circle of radius $3 \, m$ with its displacement given by $S = \frac{t^2}{2} + \frac{t^3}{3}$. The total acceleration at $t = 2 \, s$ is ....... $m/s^2$.

$A$ particle moves along an arc of a circle of radius $R$. Its velocity depends on the distance covered as $v = a\sqrt{s}$,where $a$ is a constant. Then the angle $\alpha$ between the vector of the total acceleration and the vector of velocity as a function of $s$ will be:

$A$ car is moving with a speed of $30 \,ms^{-1}$ on a circular path of radius $500 \,m$. If its speed is increasing at the rate of $2 \,ms^{-2}$, then find its acceleration. (in $\,ms^{-2}$)

$A$ car is travelling at $40\text{ m/s}$ on a circular path of radius $40\text{ m}$. It is increasing its speed at the rate of $2\text{ m/s}^2$. Its net acceleration is (in $\text{m/s}^2$) nearly (in $\text{ m/s}^2$)

Is the tangential acceleration of a particle moving in a circular path always zero? Under what condition is it zero?

In non-uniform circular motion, the ratio of radial acceleration to tangential acceleration is (where $V$ is the velocity, $r$ is the radius, and $\alpha$ is the angular acceleration).