Respuesta :
Answer: [tex]0.00636\ rad/s^2[/tex]
Explanation:
Given
CD has a playing time of [tex]t=74\ min\ or\ 74\times 60\ s[/tex]
Initial angular speed of CD is [tex]480\ rpm[/tex]
Final angular speed of DC is [tex]210\ rpm[/tex]
Angular speed, when rpm is given
[tex]\omega =\dfrac{2\pi N}{60}[/tex]
[tex]\omega_i=\dfrac{2\pi \times 480}{60}\\\\\Rightarrow \omega_i=16\pi \ rad/s[/tex]
Final speed
[tex]\Rightarrow \omega_f=\dfrac{2\pi \times 210}{60}\\\\\Rightarrow \omega_f=7\pi \ rad/s[/tex]
Using equation of angular motion
[tex]\Rightarrow \omega_f=\omega_i+\alpha t[/tex]
Insert the values
[tex]\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[/tex]
Magnitude of angular acceleration is [tex]0.00636\ rad/s^2[/tex]
