Final answer:
All points on a spinning disk have the same angular velocity because they rotate through angles at the same rate. However, the linear velocity is higher for points near the edge than for points near the center because linear velocity depends on the radius.
Step-by-step explanation:
Understanding Angular Velocity in a Spinning Disk
On a spinning disk, all points have the same angular velocity regardless of their distance from the center. This is due to the nature of angular velocity, which is defined as the rate at which an object rotates, or the time rate of change of its angular position. Angular velocity is analogous to linear velocity, but while linear velocity varies with distance from the center of rotation, angular velocity does not. In a rotating disk, because every point completes a full rotation together in the same amount of time, they all share the same angular velocity.
The linear velocity, however, depends on the radius from the center of rotation. It is given by the equation v = r × ω (v being linear velocity, r being the radius, and ω being the angular velocity). A point near the outer edge has a larger radius and hence a higher linear velocity, as it covers a larger circumference in the same period. Conversely, a point closer to the center has a smaller circumference to cover, leading to a lower linear velocity.
To specifically address the student's question, it's important to clarify that the linear velocity is not the same at all points due to varying radii (r), whereas the angular velocity (ω) is uniform for a disk spinning with constant angular velocity, as every point completes a 360-degree rotation simultaneously.