What happens once you spin a CD also fast? The answer is the it shatters. The slow Mo Guys caught some high speed video showing just how it breaks.

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What happens once you take it expensive equipment and do silly points with it? Awesome stuff is the correct answer—this is precisely what the slow-moving Mo guy did and here is the complete video. Yes, i love the sluggish Mo Guys—who doesn’t. However what ns really love is see cool things that no one saw before. The is specifically what occurred when they used a high rate camera with a turn Compact Disc. It turns out the these discs shatter as soon as you turn them also fast—with a high rate camera, you can see the propagation of product failure together the disc spins.

It’s such a good video, let’s perform some analysis.

## How quick Was the CD Spinning?

They break several CDs, yet let me look in ~ the second CD they shattered tape-recorded at 61,960 frames per second. Ns tried to usage the higher speed video, but I was getting repeating frames—not certain why. The guys insurance claim the an essential spin rate for a CD is 23,000 rpm. Let’s watch if we can get the really spin price for this wrecking CD. Yes, i am going to usage Tracker video clip Analysis—it’s free and great (do I need to keep on saying this)?

After loading the video clip into Tracker, ns can set the range by presume the diameter of a CD is 12 cm. Next, I have the right to put the origin in the center of the CD and also track some mark as it spins (before exploding). Here is what i get.

From this, I obtain an angular velocity (slope the the angle-vs-time graph) that 3.914 x 10 3 radians/second i m sorry is 37,375 rpm. This is rather a bit greater than 23,000 rpm (but of course you recognize that). Ok, one small issue. I am going through the presumption that this video clip clip shows all the frames and that each frame is certainly 1/61,960 seconds.

## Analysis of flying Stuff

Really, this is favor a standard physics question. The goes something favor this.

A human swings a ball roughly in a horizontal circle (the view over is from the top). While swinging, the cable breaks. What route does the ball follow ~ the cable breaks?

The question is frequently in a multiple-choice format, but you acquire the idea. A common answer is that the round will move away indigenous the center of the circle as soon as the cable breaks.

Let’s look in ~ the CD. What walk a item of the CD carry out after it division free? right here is a plot the the piece’s trajectory (x vs. Y).

I recognize what you space thinking: “oh look, the path of the piece is kind of curving.” Well, actually—no. The upright axis is in a lot smaller scale than the horizontal axis. This data contains some time before the piece broke off and then after ~ that, the piece was spinning together it was flung off. The piece broke off at almost the precise bottom the the CD and also so it mostly only had a horizontal velocity. Below is a plot that the x-position vs. Time because that that item (technically, I marked a edge of the piece).

Notice the it isn’t rather a constant velocity (that would certainly be a straight line in an x-t graph). Instead, this piece seems to it is in slowing down (appears—but possibly not actually slowing since I am just looking in ~ the corner of a rotate piece). From the quadratic fit, i can obtain the velocity in ~ t = 0 seconds at about 453.2 m/s (1014 mph). Is this what it should be? For an object moving in a circle (like it was at the beginning of the motion), the adhering to shows the relationship in between the angular velocity, the radius that the circle and also the linear speed.

Using one R of 0.12 m and an ω that 3.914 x 10 3 rad/s, I obtain a direct speed the 469.68 m/s. BOOM. Virtually exactly the same as from the video clip analysis. However what about the acceleration? from the quadratic fit, the CD piece has actually an acceleration of -2.138 x 10 -5 m/s 2. Why would it have an acceleration prefer that? I would guess it’s as result of air resistance. I think there is other cool here, but I am going to leaving it as a homework question (see below).

What around the rotation that the piece of the CD that paris off? If ns measure the position of 2 ends that the piece, I have the right to use those to acquire an angular orientation that the piece. Here is a plot of the edge of that item as a function of time.

This offers it an angular velocity of 6.05 x 10 3 rad/s. But why need to this piece be spinning at all? I have two guesses to start with. First, if you clock the means the CD division one end of the piece becomes complimentary before the other end. That way that the remainder of the CD is tho pulling ~ above one side of the piece which reasons it come spin top top release. My second guess has to do v angular momentum. If you think about the item while that is still linked to the CD, that piece is rotating (it goes native oriented up to down and back to up together the CD spins). If the piece has actually angular momentum before the break, it should still have angular inert after the break.

## Summary and also Homework

First, below is a diagram showing the course of a piece of the CD.

Before the CD breaks, the remainder of the CD exerts a pressure on the CD piece causing it to relocate in a one path. After the break, this force is no longer there. What execute objects without forces on lock do? The exactly answer is that they don’t readjust their momentum (velocity would certainly be acceptable). Moving in a directly line means the thing has constant velocity.

But wait! The piece does advice after the break. Yes, ns think this is due to air resistance (just a guess).

Now for some homework. There is lot to it is in done.

If a piece damaged of in such a manner the it shot straight up, would certainly you have the ability to see a change in speed due to the gravitational force? If so, might you use this acceleration to check that the framework rate is correct? If not, why not?

If over there is certainly a significant air resistance ~ above the piece of CD, deserve to you finding this pressure on other pieces too? have to a smaller sized piece have a higher or reduced acceleration as result of air resistance? estimate the mass of a piece (based top top the size) to acquire a round park figure for the acceleration because of air resistance.

Why does a broken CD item spin (or why do some spin)? try looking at various other pieces and also measure your post-break rotate rate. Do various other pieces turn the same?

Big project: track every the piece of the broken CD for a short time ~ the CD breaks. Calculation the massive of each piece based on the area density of a CD and the area that a piece. Is kinetic power conserved (should the be)? Is angular momentum conserved? do a plot of direct speed as a function of beginning distance native the center of the CD. Should this plot it is in linear?

I really want to see the answer to few of these homework questions. If you nothing answer them, i might.

Rhett Allain is an associate professor the physics in ~ Southeastern Louisiana University. The enjoys teaching and also talking about physics. Occasionally he takes things apart and also can't put them back together.

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