school
posted by Aaron on .
Two disks are spinning freely about axes that run through their respective centres (see figure below). The larger disk
(R1 = 1.42 m)
has a moment of inertia of 1180 kg · m2 and an angular speed of 4.0 rad/s. The smaller disk
(R2 = 0.60 m)
has a moment of inertia of 906 kg · m2 and an angular speed of 8.0 rad/s. The smaller disk is rotating in a direction that is opposite to the larger disk. The edges of the two disks are brought into contact with each other while keeping their axes parallel. They initially slip against each other until the friction between the two disks eventually stops the slipping. How much energy is lost to friction? (Assume that the disks continue to spin after the disks stop slipping.)

The initial angular momentum of disc 1
is I1 w1
The initial angular momentum of disc 2
is I2 w2
Add those for total angular momentum, which DOES NOT CHANGE in this problem
because there are no external moments
Afterwards the no slip condition:
R1 w1 = R2 W2
calculate the angular momentum again and find new w s
Now
Initial KE = (1/2) I1 w1^2+(1/2)I2 w2^2
Final Ke = same formula, new w s
final better be less than initial :)
find difference