Two pieces of paper are on a DVD movie disk. Paper A is farther from the center of the disk than Paper "B". The DVD disk starts to play and then starts to spin. Which statement is true?
a. Paper "A" experiences a greater tangential acceleration than Paper "B"
b. Paper "A" experiences a greater angular acceleration than Paper "B".
c. Neither statement is true.
d. Both statements are true.
I say A, am I right
To determine which statement is true, let's first understand the concepts of tangential acceleration and angular acceleration.
Tangential acceleration refers to the rate of change of an object's linear velocity as it moves along a circular path. It represents how quickly the speed of the object is changing at any given point on the circle.
Angular acceleration, on the other hand, refers to the rate of change of an object's angular velocity as it rotates around a fixed axis. It represents how quickly the object's rotational speed is changing.
In this scenario, as the DVD disk starts to spin, both Paper A and Paper B will experience the same angular acceleration since they are both attached to the same spinning disk.
However, the tangential acceleration experienced by an object depends on its distance from the center of the disk and the angular acceleration. The tangential acceleration can be calculated using the formula:
a_tangential = r * α
Where:
a_tangential is the tangential acceleration,
r is the distance from the center of the disk, and
α is the angular acceleration.
Since Paper A is farther from the center of the disk than Paper B, it has a greater distance, r, in the formula. As a result, if the angular acceleration (α) remains the same for both papers, then Paper A will indeed experience a greater tangential acceleration (a_tangential) than Paper B. Therefore, statement a. "Paper A experiences a greater tangential acceleration than Paper B" is true.
However, statement b. "Paper A experiences a greater angular acceleration than Paper B" is false, as the angular acceleration is the same for both papers since they are on the same spinning disk.
In conclusion, the correct answer is a. "Paper A experiences a greater tangential acceleration than Paper B."