Video: Converting between Linear and Angular Velocity

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. When writing along the outer edge of the disc, the angular speed of a drive is 4800 rpm (revolutions per minute). Find the linear speed if the CD has a diameter of 120 millimeters. Give your answer in millimeters per minute correct to two decimal places if necessary.

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Video Transcript

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. When writing along the outer edge of the disc, the angular speed of a drive is 4800 revolutions per minute. Find the linear speed if the CD has a diameter of 120 millimeters. Give your answer in millimetres per minute correct to two decimal places if necessary.

Well, if we take a look at the question, we can see that the angular speed of a drive is 4800 revolutions per minute. So let’s think what this means. It means that the speed is going to be 4800 revolutions of the compact disc every minute. 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. How far is one revolution?

We could find that using the formula 𝐶 is equal to 𝜋𝑑 because the circumference is the distance travelled by one revolution. So therefore, we know that the circumference is gonna be equal to 𝜋 multiplied by 120. So therefore, we know that the circumference is gonna be 120𝜋 millimetres. And we keep millimetres in there because I’m gonna show you how this works by using the units of measurement.

So now, let’s think about this logically. We know that the angular speed is 4800 revolutions. And that’s per minute. So I’m gonna write that as 4800 rev and then divide it by one cause that’s one minute. And then, we multiply this by 120𝜋 millimeters. And that’s per revolution because that’s the distance travelled with every revolution. Then, we can see that revolutions will cancel. So what we’ve got is millimetres per minute. Well, that’s the units that we want our linear speed in.

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. Well, if we check how the question wants us to leave our answer, it wants it left to two decimal places. So therefore, if we get to the second decimal place, it’s six. Then, we look at the digit or the number to the right of this. And that’s an eight. And that is our deciding number. Well, because it’s five or above, we’re gonna round this six to a seven.

So therefore, we can say that the linear speed is going to be equal to 1809557.37 millimeters per minute. And that’s rounded to two decimal places.

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