Question

A computer hard disk starts from rest and speeds up with an angular acceleration of 190 rad/s² until it reaches its final angular speed of 7200 rpm. What is the final angular speed of the hard disk?

1) 3600 rad/s
2) 7200 rad/s
3) 120 rad/s
4) 190 rad/s

Answer 1

The final angular speed of the computer hard disk reaching 7200 rpm when converted to radians per second is approximately 753.98 rad/s. None of the provided options (3600 rad/s, 7200 rad/s, 120 rad/s, 190 rad/s) is correct.

Step-by-step explanation:

The question asks about the final angular speed of a computer hard disk that accelerates from rest with an angular acceleration of 190 rad/s² to a final speed of 7200 revolutions per minute (rpm). To answer this, we should convert the final speed from rpm to rad/s.

Firstly, we convert revolutions per minute to revolutions per second by dividing by 60:

7200 rpm ÷ 60 = 120 rps

Since one revolution is 2π radians, we then convert revolutions per second to radians per second:

120 rps × 2π rad/rev = 240π rad/s

Finally, we simplify the expression:

240π rad/s ≈ 753.98 rad/s

Therefore, the final angular speed of the hard disk in radians per second is approximately 753.98 rad/s, which is not listed in the provided options. None of the options provided (3600 rad/s, 7200 rad/s, 120 rad/s, 190 rad/s) accurately reflect the correct conversion from 7200 rpm.