Final answer:
The 200 kg machine rotating at 2000 rpm is primarily measuring its angular velocity. Angular velocity is the rotational analog of linear velocity and describes the rate of change of the rotational angle over time. Option D is correct.
Step-by-step explanation:
When a 200 kg machine is rotating at 2000 rpm, what is primarily being measured is its angular velocity. The conversion of revolutions per minute (rpm) to the SI unit of angular velocity, radians per second (rad/s), helps in the analysis of rotational motion in physics. Angular velocity is analogous to linear velocity in translational motion. It describes how fast the angle (or position) of an object is changing over time around a rotation axis.
The question about the angular analogs of linear motion can be addressed as follows:
The rotational analog of distance is rotational angle.
The rotational analog of linear velocity is angular velocity.
Angular acceleration is how much the angular velocity changes over time and is similar to linear acceleration in translational motion.
The concept of angular acceleration is crucial in understanding how the rate of rotation changes, for example, when a flywheel starts from rest and acquires a certain angular speed over a period, as well as determining the centripetal and tangential accelerations of points at a specific distance from the axis of rotation.