Question

Consider a CD spinning clockwise. What is the sum of the instantaneous velocities of two points on both ends of its diameter?

a) Zero

b) Twice the velocity of one point

c) Equal to the velocity of one point

d) Dependent on the CD's rotational speed

Answer 1

a)

Step-by-step explanation:

If you were to draw the velocity vectors for both points, they would point in opposite directions with the same magnitude, meaning that they must cancel when added.

Eg: |-x| = x, and

|x| = x,

but -x + x = 0

Answer 2

The sum of the instantaneous velocities of two points on both ends of the diameter of a spinning CD is twice the velocity of one point.

Step-by-step explanation:

The sum of the instantaneous velocities of two points on both ends of the diameter of a spinning CD is twice the velocity of one point.

The tangential speed of a point on the outer edge of the CD is greater than that of a point closer to the center. This is because the tangential speed is proportional to the distance from the center of rotation. Regardless of their distance from the center, both points will have the same angular speed.

For example, if a CD is spinning with an angular velocity of 2 radians per second, the velocity at a point on the outer edge would be 2 times the velocity at a point near the center.

Consider a CD spinning clockwise. The sum of the instantaneous velocities of two points on both ends of its diameter is zero. This is because the two points on opposite ends of the diameter are moving in opposite directions with equal magnitude of velocity.

As vectors, their velocities would cancel each other out when added. No matter the rotational speed of the CD, one point moves clockwise while the other moves counterclockwise, both with the same linear velocity but in opposite directions.