Question

A compact disc (CD) is played by a cd player, which uses a laser to read the tracks on the disc. The disc spins initially at approximately 200 rotations per minute (rpm), and increases to a maximum of approximately 500 rpm as the laser spirals inward towards the center of the disc. This ensures that the laser covers equal distance in an equal amount of time during playback. During the time that the cd is played, which of the following statements is true?

a. The laser tracking mechanism experiences a changing tangential velocity
b. The laser tracking mechanism experiences a constant angular velocity
c. The laser tracking mechanism experiences a non-zero angular acceleration
d. The laser tracking mechanism experiences a non-zero tangential acceleration

Answer 1

a. The laser tracking mechanism experiences a changing tangential velocity

c. The laser tracking mechanism experiences a non-zero angular acceleration

d. The laser tracking mechanism experiences a non-zero tangential acceleration

Step-by-step explanation:

a. The laser tracking mechanism experiences a changing tangential velocity

This is because the tangential velocity v = rω where r = radius of disc and ω = angular speed of discs. Since r is constant, v ∝ ω.

Since the angular speed changes from 200 rpm to 500 rpm, thus, the tangential velocity would also change.

So, the laser tracking mechanism experiences a changing tangential velocity

c. The laser tracking mechanism experiences a non-zero angular acceleration

Since angular acceleration, α = Δω/Δt where Δω = change in angular speed and Δt = change in time.

Since there is a change in angular speed from 200 rpm to 500 rpm in time Δt, there is thus a non-zero angular acceleration.

So, The laser tracking mechanism experiences a non-zero angular acceleration

d. The laser tracking mechanism experiences a non-zero tangential acceleration

Since tangential acceleration, a = rα where r = radius of disc and α = angular acceleration.

Since there is an angular acceleration of the disc, there is thus going to be a tangential acceleration given by a = rα.

So, the laser tracking mechanism experiences a non-zero tangential acceleration

Statement b is false because, the disc experiences a changing angular speed from 200 rpm to 500 rpm.