$A$ 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 $\,ms^{-2}$)

$A$ particle at rest starts moving with a constant angular acceleration of $4 \ rad/s^2$ in a circular path. At what time will the magnitudes of its tangential acceleration and centrifugal acceleration be equal (in $s$)?

In a hypothetical ring-shaped satellite rotating in space, artificial gravity can be achieved using centripetal force. If the satellite has a radius of $10 \,m$, then to achieve a centripetal acceleration at a point on the circumference of $10 \,ms^{-2}$, its angular speed is:

$A$ car is travelling at $30 \,ms^{-1}$ speed on a circular road of radius $300 \,m$. If its speed is increasing at the rate of $4 \,ms^{-2}$, then its acceleration is (in $\,ms^{-2}$)

$A$ particle moves in a circular path of radius $R$ with an angular velocity $\omega = a - bt$,where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $t = \frac{2a}{b}$ is:

$A$ particle of mass $m$ describes a circle of radius $r$. The centripetal acceleration of the particle is $4/r^2$. What will be the momentum of the particle?