A computer hard disk starts from rest, then speeds up with an angular accelerati

Question

A computer hard disk starts from rest, then speeds up with an angular acceleration of 200.0 rad/s2 until it reaches a final angular speed of 7000.0 rpm.

(a) What is the final angular speed in unit of rad/s ? ans.733.0
(b) How long does it take for the disk to reach this angular speed? ans 3.67

(c) How many revolutions (not radians) does it make in getting to the final angular speed? ______rev

(d) Once the disk reaches its final angular speed, it continues rotating at this same speed. How many revolutions has the disk made 10.0 s after it started up from rest? NOTE: The 10.0 s includes the time to take the disk to get up to full speed, and any additional time to get to 10.0 total seconds. Make sure your answer is in revolutions
___________rev

Explanation / Answer

Given f = 7000 rpm = 7000/60 = 116.66 rev/sec
=>(final) = 2f = 2 x 3.14 x 116.66 = 732.62 = 733 rad/sec Let it take t sec to reach its final speed

=>By (final) = (initial) + t
=>732.62 = 0 + 200 x t
=>t = 3.667 = 3.67 sec

By = (initial) x t + 1/2t^2
=> = 0 + 1/2 x 200 x (3.67)^2
=> = 1346.89 rad
Let the no. of revolution was n1
=>n x 360 = 1346.89 x (180/)
=>n = 214.364

let the no. of revolutions in (10-3.67) = 6.33 sec is n2
=>n2 = 116.66 x 6.33 = 738.45
=>Total number of revolutions(N) in 10 sec = n1+n2 = 214.364 + 738.45 = 952.81 rev

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