Angular acceleration of a computer disk drive

In summary, the problem involves a computer disk drive with constant angular acceleration starting from rest. The second revolution takes 0.640 seconds to complete. To find the time of the first revolution, the problem can be split into two parts, with two unknowns in each part. By considering the initial and final angular velocities of the first and second revolutions, an equation can be formed with only one unknown, the angular acceleration. Solving for this value allows for the calculation of the time for the first revolution.
  • #1
elsternj
42
0

Homework Statement


A computer disk drive is turned on starting from rest and has constant angular acceleration.
If it took 0.640s for the drive to make its second complete revolution, how long did it take to make the first complete revolution?



Homework Equations


[tex]\theta[/tex]=[tex]\theta[/tex]i+[tex]\omega[/tex]i1/2[tex]\alpha[/tex]t2
[tex]\omega[/tex]=+[tex]\alpha[/tex]t




The Attempt at a Solution


Okay I looked this question up on these forums and found it, and what people were saying to do was just not working so see if you can steer me in the right direction.

[tex]\theta[/tex]=[tex]\theta[/tex]i+[tex]\omega[/tex]i1/2[tex]\alpha[/tex]t2

12.56(rads) = 1/2[tex]\alpha[/tex](.64)2
solve that for [tex]\alpha[/tex]
and you get [tex]\alpha[/tex] =61.3 (now i know this acceleration is wrong because it's supposed to be 5.26)

i would then put the acceleration in a new equation and solve for 6.28 rads but the acceleration isn't even right. why?
 
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  • #2
It takes .64 seconds for the second revolution only. Break the problem into 2 sections starting with the second revolution you will end up with 2 unknowns. Now focus on the first revolution it will also have 2 unknowns but the final angular velocity for the first revolution will be the initial angular velocity for the second revolution. You can solve for the angular acceleration which is indeed 5.26/s^2. Plug that value into the equation for the first revolution and you are there.
 
  • #3
I am still feeling a little lost on this one. I can't find the acceleration because I need the initial velocity during the second rotation. I can't find the final velocity of the first rotation because i don't know the acceleration. I need a little more guidance with this one
 
  • #4
Start with the second revolution: you know time and 2Pi radians you don't know initial angular velocity or angular acceleration. So you have got an equation with 2 unknowns in it. You need another equation. Look at the first revolution. You know it travels 2pi, it's initial angular velocity is 0. But you don't know final angular velocity or angular acceleration. BUT the final angular velocity of the first revolution is the initial angular velocity for the second revolution. Now you have one equation with one unknown, the angular acceleration. You can use that value to find the time of the first revolution.
 
  • #5



I would first clarify that the given information is not enough to accurately determine the angular acceleration of the computer disk drive. We need to know the initial angular velocity and the final angular velocity in order to use the equation \omega=\omega_0+\alpha t. Without these values, we cannot accurately solve for \alpha or determine the time it takes to complete the first revolution.

Additionally, the equation \theta=\theta_0+\omega_0t+\frac{1}{2}\alpha t^2 is used for constant angular acceleration, but in this case, the angular acceleration is not constant as the drive starts from rest. We would need to use the equation \theta=\frac{1}{2}(\omega_0+\omega)t to solve for the total angle rotated after a given time t.

In order to accurately solve this problem, we would need more information such as the initial and final angular velocities. Without this information, we cannot provide an accurate response.
 

What is angular acceleration?

Angular acceleration is the rate of change of angular velocity of an object. It is a measure of how quickly an object's angular velocity is changing over time.

How is angular acceleration different from linear acceleration?

Angular acceleration is a measure of how quickly an object's rotational speed is changing, while linear acceleration is a measure of how quickly an object's linear speed is changing.

How is angular acceleration measured?

Angular acceleration is measured in units of radians per second squared (rad/s^2) or degrees per second squared (deg/s^2).

Why is angular acceleration important for a computer disk drive?

In a computer disk drive, the platters (disks) rotate at high speeds. Angular acceleration helps to maintain the stability and accuracy of the disks' rotation, which is essential for proper functioning of the drive.

How does angular acceleration affect the performance of a computer disk drive?

If the angular acceleration is too high, it can cause the disks to vibrate, which can lead to data errors and affect the overall performance of the drive. On the other hand, too low angular acceleration can result in slow read/write speeds and decreased efficiency.

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