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

$A$ car is moving with a speed of $30 \ m/s$ on a circular path of radius $500 \ m$. Its speed is increasing at the rate of $2 \ m/s^2$. What is the acceleration of the car in $m/s^2$?

$A$ disc is rotating with constant angular velocity $\omega$ about an axis passing through centre $C$ and perpendicular to the plane of the disc. An insect is moving over the disc along the radial direction with constant velocity $v$ with respect to the disc. The acceleration of the insect at the instant when its distance from the centre is $r$ will be :-

The distance of a particle moving on a circle of radius $12 \, m$ measured from a fixed point on the circle and measured along the circle is given by $s = 2t^3$ (in meters). The ratio of its tangential to centripetal acceleration at $t = 2 \, s$ is .........

For a particle in a non-uniform accelerated circular motion:

$A$ car is moving at a speed of $40\,m/s$ on a circular track of radius $400\,m.$ This speed is increasing at the rate of $3\,m/s^2.$ The acceleration of the car is ........ $m/s^2$.