Final answer:
In the case of uniform angular velocity, the angular acceleration is zero because the angular velocity is constant. A non-zero angular acceleration would imply a change in angular velocity, which is not consistent with uniform motion.
Step-by-step explanation:
When a disc rotates with uniform angular velocity, it means that the rate at which the disc turns is constant. Under these conditions, the angular acceleration, which is the rate of change of angular velocity, should be zero. If the angular acceleration were non-zero and remained the same, this would imply that the disc's angular velocity is changing, which contradicts the notion of uniform angular velocity. Therefore, the statement that 'the angular acceleration is non-zero and remains the same' is not true when a disc rotates with uniform angular velocity.
In the context of rotational kinematics, when an object is in uniform circular motion, it exhibits motion in a circle at constant speed and hence maintains a constant angular velocity without any angular acceleration. Only when an external net torque is applied to the system, resulting in a change in rotational velocity, does the object experience angular acceleration.