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 accelerati

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

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1 year 2021-07-12T11:45:28+00:00 1 Answers 61 views 0

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.