The angular velocity of a body changes from $6 \ rad \ s^{-1}$ to $21 \ rad \ s^{-1}$ in a time of $1.5 \ s$. If the moment of inertia of the body is $100 \ g \ m^2$,then the rate of change of angular momentum of the body is (in $N \ m$)

Obtain the relation between angular momentum of a particle and torque acting on it.

$A$ solid sphere of mass $2 \,kg$ and radius $1 \,m$ is free to rotate about an axis passing through its centre. $A$ constant tangential force $F$ is required to rotate the sphere with $10 \,rad/s$ in $2 \,s$ starting from rest. The value of $F$ is . . . . . . (in $\,N$)

The engine of a motor vehicle develops a power of $100 \, kW$. If it rotates at a speed of $1800 \, rpm$,the torque exerted by it is ...... $N-m$.

The moment of inertia of a body about a given axis is $1.2 \ kg \cdot m^2$. Initially,the body is at rest. To produce a rotational kinetic energy of $1500 \ J$,an angular acceleration of $25 \ rad/s^2$ must be applied to the body for a duration of ........ $(s)$.

$A$ flywheel gains a speed of $540\ r.p.m.$ in $6\ s$. Its angular acceleration will be