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A computer hard disk starts from rest, then speeds up with an angular acceleration of 190 rad/s2 until it reaches its final angular speed of 7200 rpm. part a how many revolutions has the disk made 10.0 s after it starts up?

Respuesta :

carlosego
The first thing we are going to do is find the equation of motion:
 ωf = ωi + αt
 θ = ωi*t + 1/2αt^2
 Where:
 ωf = final angular velocity
 ωi = initial angular velocity
 α = Angular acceleration
 θ = Revolutions.
 t = time.
 We have then:
 ωf = (7200) * ((2 * pi) / 60) = 753.60 rad / s
 ωi = 0
 α = 190 rad / s2
 Clearing t:
 753.60 = 0 + 190*t
 t = 753.60 / 190
 t = 3.97 s
 Then, replacing the time:
 θ1 = 0 + (1/2) * (190) * (3.97) ^ 2
 θ1 = 1494.51 rad
 For (10-3.97) s:
 θ2 = ωf * t
 θ2 = (753.60 rad / s) * (10-3.97) s
 θ2 = 4544,208 rad
 Number of final revolutions:
 θ1 + θ2 = (1494.51 rad + 4544.208 rad) * (180 / π)
 θ1 + θ2 = 961.57 rev
 Answer:
 the disk has made 961.57 rev 10.0 s after it starts up
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The equation of motion is:

[tex]wf = wi + \alpha t[/tex]

θ [tex]= wi*t+1/2\alpha t^2[/tex]

Information

wf = final angular velocity

wi = initial angular velocity

α = angular acceleration

θ = Acceleration angle θ = Revolution.

t = time.

then:

[tex]wf = (7200) * \frac{2*pi}{60} = 753.60 \frac{rad}{s}[/tex]

[tex]wi = 0[/tex]

[tex]\alpha = \frac{190 rad}{s2}[/tex]

Clearing t:

[tex]753.60 = 0 + 190 * t[/tex]

[tex]t = \frac{753.60}{190} \\t = 3.97s[/tex]

Then, change the time:

θ1 [tex]= 0 + (\frac{1}{2}) * (190) * (3.97) ^ 2[/tex]

θ1 [tex]= 1494.51 rad[/tex]

(10-3.97) s:

θ2 [tex]= wf * t[/tex]

θ2 [tex]= (753.60 \frac{rad}{s}) * (10-3.97) s[/tex]

θ2 [tex]= 4544,208 rad[/tex]

Number of final rounds:

θ1 + θ2 [tex]= (1494.51 rad + 4544,208 rad) * (180/n)[/tex]

θ1 + θ2 [tex]= 961.57 revolution[/tex]

So the number of hard disk turns is 961.57 revolutions in the first 10 seconds begins

Further explanation

The need for computer systems with increasingly high capabilities seems to be in line with current technological developments. See, computer memory chip manufacturers continue to create products that have higher speeds. At the same time, manufacturers of data storage containers or hard disk drives (HDD) have also increased the capacity and capabilities of their products.

Generally, the ability to read HDD data is currently 5,400 RPM and 7,200 RPM. But, now HDD manufacturers have begun to reach the speed of 10,000 RPM, even 15,000 RPM. One of the producers who play in this market is Western Digital (WD). Since last year, they released a 450 Gigabyte (GB) and 600 GB WD VelociRaptor product with a speed of 10,000 RPM. This SATA-based HDD is specifically designed for blade servers, high-performance personal computers (PCs), Mac computers, professional workstations, and rack servers.

RPM is a unit of calculating the speed of a hard disk. RPM is also called Rotary Per Minute or Motor Rotating Speed ​​to play HDD disk in 1 minute.

The difference in HDD rotation speed greatly affects the results obtained. HDDs have different speeds. The most popular figures are 5400 RPM and 7200 RPM. From the numbers above it means that our HDD has a speed of 5400 revolutions in 1 minute or 7200 revolutions in 1 minute.

Learn More

HDD Rotation https://brainly.com/question/8653263

Rotation speed https://brainly.com/question/8653263

Details

Class: High School

Subject: Computers and Technology

Keywords: HDD, rotation, speed

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