Conservation of angular momentum in an inelastic collision?

  • Thread starter mot
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  • #1
mot
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Homework Statement


On a frictionless table, a glob of clay of mass 0.380 kg strikes a bar of mass 0.9 kg perpendicularly at a point 0.550 m from the center of the bar and sticks to it.
a) a) If the bar is 1.300 m long and the clay is moving at 8.100 m/s before striking the bar, what is the final speed of the center of mass? (Got this, 2.405m/s)
b)At what angular speed does the bar/clay system rotate about its center of mass after the impact (in rad/s)?

Homework Equations



Li=Lf
L=r x p =mrv (when theta = 90, as in this case)
L=Iw
I of a rod = (ML2)/12
xcenter of mass=Ʃmx/Ʃm

The Attempt at a Solution


m = mass of clay
M=mass of bar
u=clay's initial speed
r=the distance from the clay to the new CM

So I set one end of the bar as x=0 and the other as x=1.3 to calculate CM
CM=((0.38)(0.65+0.55)+(0.65)(0.9))/(0.9+0.38)=0.81328m from the end of the bar
r=1.2-0.81328=0.3867m

Initial angular velocity=mru
Final " "=((1/12)ML2+mr2
so ω=(mru)/((1/12)(ML2+mr2)
When I plug in my values, I get the wrong answer, it is supposed to be 5.73. Where am I going wrong? I have spent hours at this :( I'm so frustrated!

Homework Statement





Homework Equations





The Attempt at a Solution

 
Last edited:

Answers and Replies

  • #2
ehild
Homework Helper
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1,913

Homework Statement


On a frictionless table, a glob of clay of mass 0.380 kg strikes a bar of mass 0.9 kg perpendicularly at a point 0.430 m from the center of the bar and sticks to it.
a) a) If the bar is 1.300 m long and the clay is moving at 8.100 m/s before striking the bar, what is the final speed of the center of mass? (Got this, 2.405m/s)
b)At what angular speed does the bar/clay system rotate about its center of mass after the impact (in rad/s)?

Homework Equations



Li=Lf
L=r x p =mrv (when theta = 90, as in this case)
L=Iw
I of a rod = (ML2)/12
xcenter of mass=Ʃmx/Ʃm

The Attempt at a Solution


m = mass of clay
M=mass of bar
u=clay's initial speed
r=the distance from the clay to the new CM

So I set one end of the bar as x=0 and the other as x=1.3 to calculate CM
CM=((0.38)(0.65+0.55)+(0.65)(0.9))/(0.9+0.38)=0.81328m from the end of the bar
r=1.2-0.81328=0.3867m

Where are the data in red come from?

Initial angular velocity=mru
Final " "=((1/12)ML2+mr2

You need the moment of inertia with respect to the new CM. (1/12)ML2 is the moment of inertia with respect to the centre of the rod.


ehild
 
  • #3
mot
9
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Sorry I made a typo in the question, 0.43 should have been 0.55. I've fixed it now. (1.2 is 0.65+0.55, the "position" of the clay on the rod with respect to the end).

That's what I was thinking with the moment of inertia...but doesn't adding the mr^2 take that into account?
I could also do I=Ʃmr^2, where r is the distance from the new CM
=(0.9)(0.81328-0.65)^2+(0.38)(0.3867)^2=0.0808

and my old I=((1/12)(0.9)(1.3^2)+(0.38)(0.3867^2))=0.1836

The new I gives me 14.7rad/s when I plug it into the equation:(
 
  • #5
D H
Staff Emeritus
Science Advisor
Insights Author
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That's what I was thinking with the moment of inertia...but doesn't adding the mr^2 take that into account?
No. That's the blob of clay's contribution to the moment of inertia of the bar+clay system. The bar's contribution is the moment of inertia of the bar about the combined center of mass.

Hint: Parallel axis theorem.
 
  • #6
mot
9
0
Thanks so much guys, I got it! It seemed so obvious this morning, I guess that's why you shouldn't do physics at 2am. I was comparing it to a question I had done with a mass on a rotating disc, forgetting that the disc was still rotating about the central axis
 

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