In the absence of external torque, which of the following will decrease when moment of inertia increases?

When considering rotational dynamics, the relationship between moment of inertia, angular momentum, and angular velocity is crucial. Angular momentum is defined as the product of moment of inertia and angular velocity. This can be expressed by the equation:

Angular Momentum (L) = Moment of Inertia (I) × Angular Velocity (ω)

In a scenario where there is no external torque acting on the system, the angular momentum must remain constant due to the conservation of angular momentum. If the moment of inertia increases while angular momentum remains constant, it follows that the angular velocity must decrease to maintain this balance.

Thus, an increase in moment of inertia results in a decrease in angular velocity since the product of these two quantities (moment of inertia and angular velocity) must equal a constant value (the constant angular momentum in the absence of external torques). This relationship highlights that as the distribution of mass moves further from the axis of rotation (leading to a higher moment of inertia), the speed at which the object can rotate (angular velocity) must decrease to satisfy the conservation of angular momentum.