$A$ particle is moving with constant angular acceleration $4 \text{ rad/s}^2$ in a circular path. At what time will the magnitudes of its tangential acceleration and centripetal acceleration be equal (in $\text{ s}$)?

Certain neutron stars are believed to be rotating at about $1 \, rev/sec$. If such a star has a radius of $20 \, km$,the acceleration of an object on the equator of the star will be:

$A$ ball is spun with angular acceleration $\alpha = 6t^2 - 2t$,where $t$ is in seconds and $\alpha$ is in $rad/s^2$. At $t = 0$,the ball has an angular velocity of $10 \ rad/s$ and an angular position of $4 \ rad$. The most appropriate expression for the angular position of the ball is:

If the position vector of a particle is $\vec{r} = (3\hat{i} + 4\hat{j}) \text{ m}$ and its angular velocity is $\vec{\omega} = (\hat{j} + 2\hat{k}) \text{ rad/s}$,then its linear velocity is (in $\text{m/s}$):

The angular acceleration of a wheel is $3 \ rad/s^2$. If its initial angular velocity is $2 \ rad/s$,what is the angular displacement (in $rad$) covered by it in $2 \ s$?

$A$ wheel rotates with an angular acceleration of $3 \ rad \ s^{-2}$ and an initial angular velocity of $2 \ rad \ s^{-1}$. What will be its angular displacement after $2 \ s$?