Question

Let's begin with the angular acceleration of a compact disk (CD). To play music the CD must rotate at high speed while a laser reads data encoded in a spiral pattern on the disk. The disc has radius R=6.0cm=0.060m; when data are being read, it spins at 7200 rev/min. What is the CD's angular velocity ω in radians per second? How much time is required for it to rotate through 90∘? If it starts from rest and reaches full speed in 4.0 s, what is its average angular acceleration?

Answer 1

Answer:

$\omega = 754 rad/s$

$t = 6.6 \times 10^{-4} s$

$\alpha = 188.5 rad/s^2$

Explanation:

Frequency of the disc is given by the

$f = 7200 rev/min$

here we know that

$f = \frac{7200}{60} rev/s$

$f = 120 rev/s$

now we have

$\omega = 2\pi f$

$\omega = 2\pi(120) = 754 rad/s$

Now we know that its angular speed is 754 rad/s

now to find the time to turn by 90 degree is given as

$t = \frac{\theta}{\omega}$

$t = \frac{\pi/2}{740} = 6.6 \times 10^{-4} s$

Now the angular acceleration is given as

$\alpha = \frac{\omega_f - \omega_i}{t}$

$\alpha = \frac{240\pi - 0}{4}$

$\alpha = 188.5 rad/s^2$