A constant external torque `tau` acts for a very brief period `/_\t` on a rotating system having moment of inertia `I` then

Options

A. The angular momentum of the system will change by `tau Deltat`
B. The angular velocity of the system will change by `(tauDeltat)/I`
C. If the system was initially at rest, it will acquire rotational kinetic energy `(tauDeltat)^(2)/(2I)`
D. The kinetic energy of the system will change by `(tauDeltat)^(2)/I`

Answer

A, B, C

Explanation

Let L= angular momentum
`tau = (dL)/(dt)` or `dL= tau dt`
For constant torque,
`DeltaL = tau Deltat = I Deltaomega` or `Iomega` if `omega_(i)=0`
Rotational kinetic energy `=1/2 Iomega^(2) = (DeltaL)^(2)/(2I)`