The angular speed of a flywheel moving with uniform angular acceleration changes from $1200\,rpm$ to $3120\,rpm$ in $16\,s$. The angular acceleration in $rad/s^{2}$ is: (in $\pi$)

$A$ particle moves along a circle of radius $r$ with constant tangential acceleration. If the velocity of the particle is $v$ at the end of the second revolution after the motion has started,then the tangential acceleration is

$A$ wheel,initially at rest,is rotated with a uniform angular acceleration. The wheel rotates through an angle ${\theta _1}$ in the first $1 \ s$ and through an additional angle ${\theta _2}$ in the next $1 \ s$. The ratio $\frac{{\theta _2}}{{\theta _1}}$ is

The relative angular speed of the hour hand and the second hand of a clock is (in $rad/s$):

$A$ particle at rest starts moving with constant angular acceleration '$\alpha$' in a circular path of radius '$r$'. At a certain instant, the magnitude of centripetal acceleration is $(1/3)^{rd}$ the tangential acceleration. The relation between linear speed $(V)$ and angular acceleration $(\alpha)$ is

$A$ particle is revolving in a circular path of radius $25 \, m$ with a constant angular speed of $12 \, rev/min$. The angular acceleration of the particle is .......... $rad/s^2$.