Final answer:
Angular acceleration is negative when an object rotating in a counterclockwise direction is slowing down. The object will continue spinning at the same angular velocity when the net torque acting on it is zero. The correct answer to when angular acceleration is negative is option b) When the object is slowing down.
Step-by-step explanation:
Angular acceleration is defined as the rate of change of angular velocity. In rotational motion, angular acceleration is considered negative when an object that is rotating in a counterclockwise direction (which is conventionally considered the positive direction) starts to slow down. Looking at the options given in the question, the correct answer regarding when angular acceleration is negative is: b) When the object is slowing down. They key thing to remember is that negative angular acceleration indicates a decrease in the speed of rotation. This is analogous to linear motion where deceleration, or negative acceleration, implies that an object is slowing down.
An object will continue spinning at the same angular velocity when the net torque acting on it is zero, as external forces or torques are required to change the angular velocity of an object. Therefore, for constant angular velocity, angular acceleration must be zero, and hence no net torque is acting on the object. This situation is described in option a) When net torque acting on it is zero of the second part of the question.