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When burning data to a writable compact disc, the drive adjusts the angular speed in order to keep the linear speed constant where the data is being written.
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When writing along the outer edge of the disc, the angular speed of a drive is 4800 revolutions per minute.
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Find the linear speed if the CD has a diameter of 120 millimeters.
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Give your answer in millimetres per minute correct to two decimal places if necessary.
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Well, if we take a look at the question, we can see that the angular speed of a drive is 4800 revolutions per minute.
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So let’s think what this means.
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It means that the speed is going to be 4800 revolutions of the compact disc every minute.
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Well, if we want to find the linear speed, then what we wanna do is find out how far it’s actually going to travel, well, 4800 revolutions per minute.
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How far is one revolution?
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We could find that using the formula 𝐶 is equal to 𝜋𝑑 because the circumference is the distance travelled by one revolution.
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So therefore, we know that the circumference is gonna be equal to 𝜋 multiplied by 120.
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So therefore, we know that the circumference is gonna be 120𝜋 millimetres.
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And we keep millimetres in there because I’m gonna show you how this works by using the units of measurement.
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So now, let’s think about this logically.
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We know that the angular speed is 4800 revolutions.
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And that’s per minute.
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So I’m gonna write that as 4800 rev and then divide it by one cause that’s one minute.
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And then, we multiply this by 120𝜋 millimeters.
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And that’s per revolution because that’s the distance travelled with every revolution.
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Then, we can see that revolutions will cancel.
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So what we’ve got is millimetres per minute.
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Well, that’s the units that we want our linear speed in.
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So therefore, to work out the value of our linear speed, we can do 4800 multiplied by 120𝜋, which is gonna be equal to 1809557.36846 et cetera millimeters per minute.
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Well, if we check how the question wants us to leave our answer, it wants it left to two decimal places.
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So therefore, if we get to the second decimal place, it’s six.
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Then, we look at the digit or the number to the right of this.
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And that’s an eight.
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And that is our deciding number.
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Well, because it’s five or above, we’re gonna round this six to a seven.
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So therefore, we can say that the linear speed is going to be equal to 1809557.37 millimeters per minute.
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And that’s rounded to two decimal places.