Final answer:
It takes 2 seconds for the CD player to reach its full speed of 8590 rpm with an angular acceleration of 450 rad/s^2.
Step-by-step explanation:
To calculate how long it takes for a CD player to reach its full speed from rest with given angular acceleration, we can use the kinematic equation for angular motion: \(\omega = \omega_0 + \alpha t\), where \(\omega\) is the final angular velocity, \(\omega_0\) is the initial angular velocity (which is 0 for starting from rest), \(\alpha\) is the angular acceleration, and t is the time. We need to convert the final velocity from rpm to rad/s for consistency with the angular acceleration units.
First, convert 8590 rpm to rad/s: 8590 rpm * (2\(\pi\) rad/1 rev) * (1 min/60 s) = 899.92 rad/s. Now we have \(\omega\) = 899.92 rad/s, \(\omega_0\) = 0 rad/s, and \(\alpha\) = 450 rad/s2.
Plug in the values to calculate t: 0 + 450 rad/s2 * t = 899.92 rad/s t = 899.92 rad/s / 450 rad/s2 = 2 s.
Therefore, it takes 2 seconds for the CD player to reach its full speed of 8590 rpm from rest with an angular acceleration of 450 rad/s2.