Conservation of Angular Momentum

1
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.

2
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.
3
Treat the CD as a disk
Treat the gum as a point mass
The gum colliding with the CD is the event and
4
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
5
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
6
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.