A hard drive on a modern computer spins at 10000 rpm (revolutions per minute). If the driver is designed to start from rest and reach operating speed in 1.4 s, what is the angular acceleration of the disk?
To find the angular acceleration of the disk, we can use the formula:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time
First, let's convert the rotational speed from revolutions per minute (rpm) to radians per second (rad/s).
To convert from rpm to rad/s, we need to multiply by 2π (to convert revolutions to radians) and divide by 60 (to convert minutes to seconds):
Angular velocity (ω) = (10000 rpm) * (2π rad/rev) / (60 s/min)
= 10000 * 2π / 60 rad/s
≈ 1047 rad/s
Now, we have the initial angular velocity.
The final angular velocity can be determined by the formula:
Final angular velocity (ωf) = (Change in angular position) / Time
Since the disk starts from rest and reaches operating speed, the change in angular position is 2π radians (one complete revolution).
Final angular velocity (ωf) = (2π rad) / (1.4 s)
≈ 4.487 rad/s
Now we can calculate the angular acceleration using the formula mentioned earlier:
Angular acceleration (α) = (4.487 rad/s - 0 rad/s) / 1.4 s
≈ 3.205 rad/s²
Therefore, the angular acceleration of the disk is approximately 3.205 rad/s².