$A$ wheel starting from rest is uniformly accelerated at $2 \, rad/s^2$ for $20 \, s$. It is allowed to rotate uniformly for the next $10 \, s$ and is finally brought to rest in the next $20 \, s$. The total angle rotated by the wheel (in radians) is ............

$A$ man is sitting in a smooth groove on a horizontal circular table at the edge by holding a rope joined to the centre. The moment of inertia of the table is $I$. The mass of the man is $M$. The man now pulls the rope so that he comes to the centre. The angular velocity of the table:

The angular momentum of a rigid body of mass $m$ about an axis is $n$ times the linear momentum $(P)$ of the body. The total kinetic energy of the rigid body is:

$A$ circular platform is situated in a horizontal plane and can rotate about a vertical axis passing through its center. $A$ tortoise is sitting at one edge of the platform,and the platform is rotating with a constant angular velocity $\omega_0$. If the tortoise starts moving with a uniform speed along a chord of the circular platform,how will the angular velocity of the platform change with time $t$?

$A$ body weighs $6$ g when placed in one pan and $24$ g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty,the true weight of the body is ....... g.

$A$ horizontal platform is rotating with a uniform angular velocity about a vertical axis passing through its center. At some instant, a viscous liquid of mass $m$ is dropped at its center, which is free to spread and eventually falls off the edge. During this time interval, the angular velocity