Question

A certain CD has a playing time of 76 minutes. When the music starts, the CD is rotating at an angular speed of 4.10 × 10 2 4.10×102 revolutions per minute (rpm). At the end of the music, the CD is rotating at 2.90 × 10 2 2.90×102 rpm. Find the magnitude of the average angular acceleration of the CD. Express your answer in rad/s².

Answer 1

Answer:

average acceleration =   2.74 x 10⁻³ rad/s²

Explanation:

given,

CD playing time = 76 minutes

initial angular speed of CD = 4.10 × 10² rev/min

                                             = $4.1 \times 10^2\times \dfrac{2 \pi}{60}$

                                             = 42.9 rad/s

final angular speed of CD = 2.90 × 10² rev/min

                                           = $2.9 \times 10^2\times \dfrac{2 \pi}{60}$

                                           = 30.37 rad/s

average acceleration = $\dfrac{\omega_f-\omega_i}{t}$

                                   =  $\dfrac{30.37 -42.9}{76\times 60}$

average acceleration =  0.00274 rad/s²

average acceleration =  2.74 x 10⁻³ rad/s²