MHB Finding a radius when an angular speed in RPM is given

[bsmithysmith]

When being burned in a writable CD-R Drive, the angular speed is often faster when playing audio... When writing along the outer edge, the angular speed of one drive is about 4800 RPM (Revolutions per minute). Find the linear speed.

The question above it, or before this one was with CD's radius is 60mm and the RPM is 200 but this time I'm not given the Radius. On that previous problem, it took me awhile to figure out after seeing the answer at the back of the book that the linear speed is approximated to 75,000.000 mm/min. (just giving part of the final answer). What I did to get that answer was multiply $$2pi$$ by the RPM, 200, because an entire revolution IS 2pi. Then I multiplied the answer by the radius. All in all it was pretty much:

$$Velocity = RPM(2pi)(Radius)$$

I still don't understand how that equation links to the answer; it's not clicking in my head why and how velocity is linked to circumference multiplied by the RPM.

Back to the main question, how do I find the linear speed when I have not been given the radius?

$$Velocity = 9600pi(radius)$$

 

[topsquark]

When being burned in a writable CD-R Drive, the angular speed is often faster when playing audio... When writing along the outer edge, the angular speed of one drive is about 4800 RPM (Revolutions per minute). Find the linear speed.

The question above it, or before this one was with CD's radius is 60mm and the RPM is 200 but this time I'm not given the Radius. On that previous problem, it took me awhile to figure out after seeing the answer at the back of the book that the linear speed is approximated to 75,000.000 mm/min. (just giving part of the final answer). What I did to get that answer was multiply $$2pi$$ by the RPM, 200, because an entire revolution IS 2pi. Then I multiplied the answer by the radius. All in all it was pretty much:

$$Velocity = RPM(2pi)(Radius)$$

I still don't understand how that equation links to the answer; it's not clicking in my head why and how velocity is linked to circumference multiplied by the RPM.

Back to the main question, how do I find the linear speed when I have not been given the radius?

$$Velocity = 9600pi(radius)$$

Are the two problems linked? As you say, this cannot be done without the radius.

-Dan

PS Velocity has an associated direction. Speed does not. You are looking for the speed, not velocity.

 

[bsmithysmith]

Are the two problems linked? As you say, this cannot be done without the radius.

-Dan

PS Velocity has an associated direction. Speed does not. You are looking for the speed, not velocity.

My mistake, linear speed is not velocity since its distance/time whereas the one in my book is arclength/time.

The two problems are not linked despite the one I'm asking does not have a radius given. I'll ask my teacher tomorrow about it.

On the other hand, I'm still curious about how [MATH/]2pi(r)(rpm)$$ turns angular speed to linear speed.

 

[Evgeny.Makarov]

how do I find the linear speed when I have not been given the radius?

If the disk radius has not change between CDs, DVDs and Blu-ray disks, we can assume that it has not changed from one problem to the next. :)

I still don't understand how that equation links to the answer; it's not clicking in my head why and how velocity is linked to circumference multiplied by the RPM.

Let $\nu$ be the frequency measured in RPM and $r$ be the radius. Fix some time interval $t$ measured in minutes. During this time, the disk has made $\nu t$ revolutions. The point has traveled distance $d=2\pi r\cdot\nu t$. Therefore, the point's speed is $d/t=2\pi r\nu$.

 

[bsmithysmith]

Well as you pointed out, there is pretty much no way to finish it without a radius, so I just used the radius of the CD above (60mm) and I'm satisfied!