Final answer:
Positive angular velocity indicates counter-clockwise rotation, while negative angular acceleration means the angular velocity is decreasing and the object is slowing down. A figure skater spinning and then slowing to a stop is a practical example of this concept in action.
Step-by-step explanation:
When a student asks what positive angular velocity and negative angular acceleration look like, they are inquiring about the behavior of objects in rotational motion. Positive angular velocity refers to an object rotating in a counter-clockwise direction from a top view, and this is conventionally considered the positive direction in physics. Negative angular acceleration occurs when there is a decrease in the angular velocity over time, which means the object is slowing down if it was initially rotating counter-clockwise.
Picture a figure skater spinning in the counterclockwise direction; her angular velocity is positive. When this skater hits an imaginary brake, causing a large, negative angular acceleration, her rotation speed would decrease rapidly, and she would eventually come to a stop. If the skater was spinning at a stable rate and then started to spin slower, this means the change in angular velocity, or Δω, over a change in time, or Δt, is negative, reflecting the negative angular acceleration, expressed as rad/s².
Just like linear motion where an object moving forward with a positive velocity comes to a stop through negative acceleration or deceleration, rotational motion behaves similarly with angular velocity and angular acceleration. Applying a negative torque to a rotating system, which is analogous to applying brakes in a moving car, results in negative angular acceleration.