Question

A CD is spinning on a CD player. In 12 radians, the cd has reached an angular speed of 17 r a d s by accelerating with a constant acceleration of 3 r a d s 2 . What was the initial angular speed of the CD

Answer 1

Answer:

The initial angular speed of the CD is equal to 14.73 rad/s.

Explanation:

Given that,

Angular displacement, $\theta=12\ rad$

Final angular speed, $\omega_f=17\ rad/s$

The acceleration of the CD,$\alpha =3\ rad/s^2$

We need to find the initial angular speed of the CD. Using third equation of kinematics to find it such that,

$\omega_f^2=\omega_i^2+2\alpha \theta\\\\\omega_i^2=\omega_f^2-2\alpha \theta$

Put all the values,

$\omega_i^2=(17)^2-2\times 3\times 12\\\\\omega_i=\sqrt{217}\\\\\omega_i=14.73\ rad/s$

So, the initial angular speed of the CD is equal to 14.73 rad/s.