Ball rotating on axle which is rotating itself

  • #1

Homework Statement


A ball of mass m is attached via a rod of length x to an axle that rotates with angular velocity ω. You can consider the ball to be a point mass.
m = 5 kg, x = 0.3 m, y = 0.4 m, ω= 30 rad/s

(a) What is the linear momentum (direction and magnitude) of the ball?
(b) What is the angular momentum (direction and magnitude) of the ball about point A?

I've included a diagram I made.The top ball has mass m = 5 kg and the bottom ball A is rotating with angular velocity ω. Hopefully that diagram makes sense...

Homework Equations


I = mr2
L=Iω
p=mv
v=rω


The Attempt at a Solution


(a) p=mv
v=rω=0.3m*30rad/s=9m/s
p=5kg*9m/s=45kgm/s clockwise
(b) L=Iω
L=mr2ω
This is where I am confused. It would be easy to calculate if A wasn't rotating but how do I . calculate the angular momentum of the ball about point A given the fact that A is rotating?
 

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Answers and Replies

  • #2
SammyS
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Homework Statement


A ball of mass m is attached via a rod of length x to an axle that rotates with angular velocity ω. You can consider the ball to be a point mass.
m = 5 kg, x = 0.3 m, y = 0.4 m, ω= 30 rad/s

(a) What is the linear momentum (direction and magnitude) of the ball?
(b) What is the angular momentum (direction and magnitude) of the ball about point A?

I've included a diagram I made.The top ball has mass m = 5 kg and the bottom ball A is rotating with angular velocity ω. Hopefully that diagram makes sense...

Homework Equations


I = mr2
L=Iω
p=mv
v=rω


The Attempt at a Solution


(a) p=mv
v=rω=0.3m*30rad/s=9m/s
p=5kg*9m/s=45kgm/s clockwise
(b) L=Iω
L=mr2ω
This is where I am confused. It would be easy to calculate if A wasn't rotating but how do I . calculate the angular momentum of the ball about point A given the fact that A is rotating?
As I read this problem, there is only one ball. No ball at point A.

attachment.php?attachmentid=58379&d=1367386096.jpg
 
  • #3
Ah, you again. Thanks for the help! :)

I wish I could show you the diagram on my paper... it demonstrates the problem a lot better. The axle itself is rotating with angular velocity ω. There might not necessarily be a ball at the end of the axle but the point at the end of the axle is labeled A.
 
  • #4
SammyS
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Ah, you again. Thanks for the help! :)

I wish I could show you the diagram on my paper... it demonstrates the problem a lot better. The axle itself is rotating with angular velocity ω. There might not necessarily be a ball at the end of the axle but the point at the end of the axle is labeled A.
Do this mean you still haven't solved the problem ?
 
  • #5
haruspex
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A is just a point in space taken as a reference. The axle rotates about there, but points don't have rotation.
 

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