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Conservation of Angular Momentum

- Important points to consider
- The units of angular velocity, ?, are rad/s.
- Use Rev/min instead of rpm so you can see the

units cancel.

The Problem A compact disk, CD, has a mass of

15.2 g and a radius of 58.0 mm. The angular speed

varies as it reads the outmost track versus the

innermost track. Lets say a song is playing

which resides close to the middle of the CD and

it is turning at 3750 RPM. Unfortunately, a piece

of gum with a mass of 0.500 g falls onto, and

sticks to, the CD at a point midway between its

rim and center. Also, at this same instant, the

CD loses power and is freely turning. Assuming no

friction, calculate the final speed in RPM of the

CD-gum combination.

Treat the CD as a disk

Treat the gum as a point mass

The gum colliding with the CD is the event and

Lets begin by finding a few values and doing

some converting. This will make our expressions a

little cleaner later on.

Not rotating

½ of CD radius

There are two objects, so there will be two terms

for initial and two terms for final.

0

Now, because the CD and gum are stuck together,

they have a common final speed

So, the speed of the CD decreases from 393 rad/s

to 388 rad/s. The final speed corresponds to less

rotational energy than the CD had originally. The

lost energy shows up in the rotational energy

of the gum.

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