Angular Momentum: Rod on Rotating Disk

[nastassja]

Homework Statement

A uniform disk (like a record turntable) turns with a frequency of 5.2 rev/s around a frictionless spindle. A non-rotating rod of the same mass as the disk and length equal to the disk's diameter is placed on the freely spinning disk so both turn around the spindle. (I_disk = M R^2/2, I_rod = M L^2/12)

a) First consider the idealized case where the rod sticks tightly to the disk immediately upon impact. How fast does the combination turn?

f = rev/s 3.12 OK

b) More realistically, there is a frictional force between the two surfaces such that the magnitude of the torque slowing down the disk is equal to the magnitude of the torque speeding up the rod (this is a consequence of Newton's 3rd Law.). Hence we have adisk = -C arod, where a generically means angular acceleration. Find the constant C.

C = .667 OK




c) The disk slows and the rod speeds up until they are moving together. Find the frequency with which the combination turns in this case.

f' = ?

HELP: Consider the net external torque on the system. What is it? What does this imply?

d) Suppose Idisk = .65 kg m2. What is the magnitude of the kinetic energy lost due to friction?

|Wfric| = ?

HELP: Use the work-energy theorem: the work done by friction is equal to the change in kinetic energy.

Homework Equations

L=Iw
w=2pi*f
torque=Ia

The Attempt at a Solution

I got a and b and I'm now stuck on c. I know I can figure out d if I have c. I don't understand how to work this one at all. All I need is some help starting it.

 

[r34racer01]

Hi I have a very similar problem. How did u get the first to parts solving for F and C?

 

[horatio89]

c) What is the condition for the conservation of angular momentum? Does it hold in this case?

d) Compare the rotational KE of the system before and after the rod is placed on the turntable.