Question

A certain CD has a playing time of 74.0 minutes. When the music starts, the CD is rotating at an angular speed of 480 revolutions per minute (rpm). At the end of the music, the CD is rotating at 210 rpm. Find the magnitude of the average angular acceleration of the CD. Express your answer in rad/s2.

Answer 1

Answer: $0.00636\ rad/s^2$

Explanation:

Given

CD has a playing time of $t=74\ min\ or\ 74\times 60\ s$

Initial angular speed of CD is $480\ rpm$

Final angular speed of DC is $210\ rpm$

Angular speed, when rpm is given

$\omega =\dfrac{2\pi N}{60}$

$\omega_i=\dfrac{2\pi \times 480}{60}\\\\\Rightarrow \omega_i=16\pi \ rad/s$

Final speed

$\Rightarrow \omega_f=\dfrac{2\pi \times 210}{60}\\\\\Rightarrow \omega_f=7\pi \ rad/s$

Using equation of angular motion

$\Rightarrow \omega_f=\omega_i+\alpha t$

Insert the values

$\Rightarrow 7\pi =16\pi +\alpha \times 74\times 60\\\Rightarrow -9\pi =\alpha \cdot (4440)\\\\\Rightarrow \alpha=-\dfrac{9\pi}{4440}\\\\\Rightarrow \alpha=-0.00636\ rad/s^2$

Magnitude of angular acceleration is $0.00636\ rad/s^2$