Spinning spokes and clay

  • Thread starter Westin
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  • #1
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Homework Statement



A device consists of eight balls each of mass 0.78kg attached to the ends of low-mass spokes of length 2.2m, so that the radius of rotation of the balls is 1.1m. The device is mounted in the vertical plane. The axle is held up by supports that are not shown, and the wheel is free to rotate on the nearly frictionless axle. A lump of clay with mass 0.4kg falls and sticks to one of the balls at the location shown, when the spoke attached to that ball is at 45
char0E.png
to the horizontal. Just before the impact the clay has a speed 7m
char3D.png
s, and the wheel is rotating counterclockwise with angular speed 0.4rad
char3D.png
s.

1)Which of the following statements are true about the device and the clay, for angular momentum relative to the axle of the device?

Select all that are True.
a)The angular momentum of the device and clay system just after the collision is equal to the angular momentum of the device and clay system just before the collision.
b)The angular momentum of the falling clay is zero because the clay is moving in a straight line.
c)The angular momentum of the device is the same before and after the collision
d)Just before the collision the angular momentum of the wheel is zero.
e) The angular momentum of the device is the sum of the angular momenta of all eight balls.


2) Just before the impact, what is the angular momentum of the combined system of device plus clay about the center? (As usual, x
char5E.png
is to the right, y
char5E.png
is up, and z
char5E.png
is out of the page.)

Li
char7E.png
=
char1C.png
, ,
char1D.png


3) Just after the impact, what is the angular momentum of the combined system of device plus clay about the center?

Lf
char7E.png
=
char1C.png
, ,
char1D.png


4) Just after impact, what is the angular velocity of this device?

char21.png
f
char7E.png
=
char1C.png
, ,
char1D.png

[/B]


Homework Equations



L = mvr
L = I w
w = L/I[/B]


The Attempt at a Solution



For #1, I believe the answer is a) and e)

For #2, I tried Initial angular momentum of the system is the sum of the disk and clay.
L Disk = IW = .5MR^2*W (you know this quantity will be subtracted in the end since it points in the -z direction via RightHandRule)
L Clay = r x p = R(mv)
Li = Lc - Ld
so... (1.1m)(0.4kg)(7m/s) - (.5(8*0.78kg)(1.1m)^2(.4rad/s))

For #3 Since there is no net torque acting on the system, the angular momentum after will be the same as before.

For #4 Final angular velocity: W = L/I. You need to update your I though, since the system is now Disk+clay
I final = .5MR^2 + mR^2
[/B]
 

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Answers and Replies

  • #2
BvU
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Hello Westin,

Is there a question you want answered ?

If not, I have some comments:

You have no relevant equation for I . You mention ##L_{disc} = I\vec\omega## and then treat the balls as a disc. No good!

##\vec L_{clay} = \vec r \times \vec p ## is good, Rmv is not correct

Something is going wrong with the signs of your ##L##.

## \vec L_i = \vec L_{balls} + \vec L_{clay}##, not ## - ##


And a small detail for 1e: this is correct, provided you take the same distance between axis of rotation and center of ball.
Reason I bring it up is that usually (e.g. in tables) the moment of inertia around an axis through the center is given.​
 
  • #3
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Is the first part right with a) and e) being true? and also what do i do for #2 instead?
 
  • #4
haruspex
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##\vec L_i = \vec L_{balls} + \vec L_{clay}##, not − -
True, but ##\vec L_{balls}## is negative, so the following line is OK (except for the error in Idevice that you already noted).
1e: this is correct, provided you take the same distance between axis of rotation and center of ball.
Not sure what you're saying there. Are you pointing out that unless the balls are small compared with the spoke length the parallel axis theorem should be used?
 
  • #5
haruspex
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what do i do for #2 instead?
First, get the I correct for the device. It is not a uniform disk.
 
  • #6
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is it a rod? My homework is due at 8pm..
 
  • #7
haruspex
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is it a rod? My homework is due at 8pm..
You answered correctly that e) is true. What is the moment of inertia for one spoke+ball? Note this:
balls each of mass 0.78kg attached to the ends of low-mass spokes
 

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