Tangential speed problem with a hard drive disk

In summary, the objective of the problem is to find the tangential velocity on a computer hard drive disk with a diameter of 3.5 inches rotating at 7200 rpm, with the "read head" positioned halfway between the axis of rotation and the outer edge of the disk. To solve, the units are converted from inches to meters and the distance to the axis is found. The angular velocity is then calculated by dividing the angular displacement by the time, and then converted to radians/s. Finally, the tangential speed is found by multiplying the angular speed by the radius of rotation. However, it is important to divide by 60 when converting the units of minutes to seconds, and to include a factor of 2\pi when
  • #1
Spartan301
20
0

Homework Statement



A computer hard drive disk with a diameter of 3.5 inches rotates at 7200 rpm. The “read head” is positioned exactly halfway from the axis of rotation to the outer edge of the disk. What is the tangential speed in m/s of a point on the disk under the read head?

Objective: Find tangential velocity on disk.

Homework Equations


Battle plan:
Convert inches to meters
Find the distance to the axis
Find the angular velocity by dividing the angular displacement by the time.
Convert from an angular speed in rad/s to a tangential speed in m/s by multiplying the angular speed by the radius of rotation.

The Attempt at a Solution


Outcome:
0.0889m/4 = 0.022225 m
7200r/min x 60 = 432000 r/s
432000 r/s x 0.022225 m = 9601.2 m/s :(

The key says the answer is 17 m/s.

I would so appreciate any help on this problem. Thanks!
-Tom
 
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  • #2
Spartan301 said:

Homework Statement



A computer hard drive disk with a diameter of 3.5 inches rotates at 7200 rpm. The “read head” is positioned exactly halfway from the axis of rotation to the outer edge of the disk. What is the tangential speed in m/s of a point on the disk under the read head?

Objective: Find tangential velocity on disk.

Homework Equations


Battle plan:
Convert inches to meters
Find the distance to the axis
Find the angular velocity by dividing the angular displacement by the time.
Convert from an angular speed in rad/s to a tangential speed in m/s by multiplying the angular speed by the radius of rotation.

The Attempt at a Solution


Outcome:
0.0889m/4 = 0.022225 m
7200r/min x 60 = 432000 r/s
432000 r/s x 0.022225 m = 9601.2 m/s :(

The key says the answer is 17 m/s.

I would so appreciate any help on this problem. Thanks!
-Tom

Hi Tom,

Your "battle plan" is just fine. The only problem is that you should divide by 60. (The units of minutes are in the denominator.) Also, on the last line, there is a factor of [itex]2\pi[/itex] need to put the angular speed in radians/s.
 
  • #3
Thank you!
 

What is tangential speed?

Tangential speed is the speed at which an object moves along a circular path, measured at a point tangent to that path. It is also known as linear speed.

How is tangential speed related to hard drive disks?

Tangential speed is an important factor in the functioning of hard drive disks. It determines how quickly the disk can spin and how fast data can be read and written from the disk.

What factors affect the tangential speed of a hard drive disk?

The tangential speed of a hard drive disk can be affected by the rotational speed of the disk, the size of the disk, and the distance from the center of the disk to the point being measured.

How is tangential speed calculated for a hard drive disk?

Tangential speed can be calculated by multiplying the rotational speed of the disk (in revolutions per minute) by the circumference of the disk at the point being measured. This can be expressed as V = ωr, where V is tangential speed, ω is rotational speed, and r is the radius of the disk.

Why is understanding tangential speed important for hard drive disk design?

Tangential speed is important for hard drive disk design because it directly affects the performance of the disk. A higher tangential speed allows for faster data transfer and retrieval, while a lower tangential speed may result in slower performance and longer loading times.

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