In an isolated system, where no external torques act upon the rotating object, the angular momentum is conserved. The moment of inertia (I) of a rotating object is directly related to its angular momentum (L) by the equation:
L = I * ω
where ω is the angular velocity of the object.
If the moment of inertia of a rotating object is doubled while no external torques are acting on it, the angular momentum must remain constant. Let's assume the initial moment of inertia is I1 and the final moment of inertia is I2 = 2I1.
Initially: L1 = I1 * ω1 Finally: L2 = I2 * ω2 = (2I1) * ω2
Since angular momentum is conserved, we have L1 = L2, which gives:
I1 * ω1 = (2I1) * ω2
Simplifying the equation, we find:
ω2 = (I1 * ω1) / (2I1) = ω1 / 2
So, when the moment of inertia is doubled in an isolated system, the final angular velocity is half of the initial angular velocity. In other words, the angular velocity of the object is reduced by a factor of two.