Question

When the play button is pressed, a CD accelerates uniformly from rest to 460 rev/min in 2.0 revolutions.

a. What is the acceleration of the CD?
b. How long does it take for the CD to reach 460 rev/min?
c. What is the final angular velocity of the CD?
d. None of the above

Answer 1

The question requires the use of rotational kinematics equations to calculate angular acceleration, time to reach a certain angular speed, and final angular velocity of a CD when starting from rest.

Step-by-step explanation:

The question involves calculating the angular acceleration, the time taken to reach a certain angular speed, and the final angular velocity of a CD when the play button is pressed. To solve this problem, one can use the kinematic equations for rotational motion:

• ω = ω_0 + αt: This equation relates the final angular velocity (ω), initial angular velocity (ω_0), angular acceleration (α), and time (t).
• θ = ω_0t + ½αt²: This equation relates the angular displacement (θ) to the time (t), angular acceleration (α), and initial angular velocity (ω_0).

Using these equations, following are the steps to solve the given problem:

a) To find the angular acceleration, you would set θ to 2 revolutions (which is 2×2π radians), ω_0 to 0 (since the CD starts from rest), and solve for α.

b) To determine how long it takes for the CD to reach 460 rev/min, convert 460 rev/min to radians per second (by multiplying by 2π/60), and use the first kinematic equation to solve for t.

c) The final angular velocity of the CD is the one given in the problem, 460 rev/min, which can be converted to radians per second as mentioned previously.

Note that since specifics have not been provided, no numerical values are calculated here.