Final answer:
The angle made by the total acceleration of a point on a link with the link itself when the magnitude of angular acceleration is zero is 90 degrees, since all acceleration is centripetal and directed toward the center of the circular path of the link.
Step-by-step explanation:
When the magnitude of angular acceleration of a link is zero, it means the link is not experiencing any angular acceleration. In this state, provided the link is moving, it must be moving with a constant angular velocity, and any acceleration would be purely centripetal (i.e., directed towards the center of the circular path).
When the magnitude of angular acceleration of a link is zero, it means that the link is moving in a circular path with a constant angular velocity but no change in speed. In this case, the total acceleration of a point on the link is solely due to centripetal acceleration, which always points towards the center of the circular path.
The angle between the total acceleration and the link is 90° because the centripetal acceleration is always perpendicular to the velocity of the point on the link.
Therefore, the total acceleration of a point on the link at any instant would be centripetal acceleration, which is always directed radially inwards towards the center of rotation, perpendicular to the tangential velocity of the point on the link. The angle made by the total acceleration (which is centripetal under these circumstances) with the link (or tangential to the path of the point on the link) is 90 degrees(C).