The angular acceleration becomes infinite when r becomes:

Explanation

The angular acceleration becomes infinite when r approaches zero (r → 0).The angular acceleration (α) is defined as the rate of change of angular velocity (ω) with respect to time (t), or:α = dω/dtFor an object rotating about a fixed axis with a constant angular acceleration, the angular acceleration is related to the torque (τ) acting on the object and the moment of inertia (I) of the object by the equation:τ = IαWhen the radius (r) of the object approaches zero, the moment of inertia of the object also approaches zero, assuming the mass and shape of the object remain constant. This means that a finite torque applied to the object will result in an infinite angular acceleration, according to the equation above. Therefore, the angular acceleration becomes infinite when the radius of the object approaches zero.