About linear and angular momentum

[Apashanka]

Homework Statement

Homework Equations

For this problem I got the angular momentum conservation equations,
mv(l+h)=mv'(l+h)+Ml²ω
and momentum conservation equation as
mv(l+h)=mv'(l+h)
m=colliding mass,v and v' velocity before and after collision.
M=mass of the rod.
2l=length of the rod.
h=vertical distance from the centre of the rod to colliding mass.

The Attempt at a Solution

So if linear momentum is conserved ,angular momentum will not be conserved here.
But if linear momentum is conserved ,angular momentum has to be conserved(since just moment of linear momentum)
So in this case linear momentum will not be conserved ,is it??

 

[kuruman]

Homework Statement

View attachment 237754

Homework Equations

For this problem I got the angular momentum conservation equations,
mv(l+h)=mv'(l+h)+Ml²ω
and momentum conservation equation as
mv(l+h)=mv'(l+h)
m=colliding mass,v and v' velocity before and after collision.
M=mass of the rod.
2l=length of the rod.
h=vertical distance from the centre of the rod to colliding mass.

The Attempt at a Solution

So if linear momentum is conserved ,angular momentum will not be conserved here.
But if linear momentum is conserved ,angular momentum has to be conserved(since just moment of linear momentum)
So in this case linear momentum will not be conserved ,is it??

Please list the statements that may or may not be true as given by the problem.

 

[Apashanka]

So if linear momentum is conserved ,angular momentum will not be conserved here.
But if linear momentum is conserved ,angular momentum has to be conserved(since just moment of linear momentum)
So in this case linear momentum will not be conserved ,is it??

My question is just this??

 

[Apashanka]

Please list the statements that may or may not be true as given by the problem.

The statements are

 

[kuruman]

So if linear momentum is conserved ,angular momentum will not be conserved here.

Non-conservation of angular momentum is not necessarily a result of linear momentum conservation. What must be true for (a) linear momentum to be conserved regardless of whether angular momentum is or is not conserved and (b) angular momentum to be conserved regardless of whether linear momentum is or is not conserved?

 

[Apashanka]

For this problem I got the angular momentum conservation equations,
mv(l+h)=mv'(l+h)+Ml²ω
and momentum conservation equation as
mv(l+h)=mv'(l+h)

So will I be able to say that linear momentum is conserved and angular momentum doesn't??

 

[kuruman]

So will I be able to say that linear momentum is conserved and angular momentum doesn't??

On what do you base this conclusion? As I asked in #5,

What must be true for (a) linear momentum to be conserved regardless of whether angular momentum is or is not conserved and (b) angular momentum to be conserved regardless of whether linear momentum is or is not conserved?

Answer these questions first and then determine what is or is not true in this particular case.

 

[Apashanka]

On what do you base this conclusion? As I asked in #5,

From the conservation equations

For this problem I got the angular momentum conservation equations,
mv(l+h)=mv'(l+h)+Ml²ω
and linear momentum conservation equation as
mv(l+h)=mv'(l+h)

Will you please help as I have got these conservation equations.
which one is conserved and which is not.,as I find one's conservation leads to another

 

[kuruman]

From the conservation equations

Will you please help as I have got these conservation equations.
which one is conserved and which is not.,as I find one's conservation leads to another

I am trying to help you but I will not give you the answer. I am helping you by asking questions the answers to which will lead you to the answer you are seeking. So far you have not answered the questions I asked in #5 and #7. So I will ask you for a third time, under what conditionsare linear and angular momentum conserved? Please find the answers, let me know and we will take it from there.

Also your logic is fatally flawed and it seems that you don't see that. The problem asks whether linear and/or angular momentum are conserved. You cannot write down conservation equations for these quantities unless you first ascertain that these quantities are indeed conserved. Writing the equations down does not make it so. Besides, your equations are incorrectly written, but you don't need to worry about that because this is a conceptual question that requires no equations to get the answer(s).

 

[Apashanka]

under what conditionsare linear and angular momentum conserved?

If F_external=0,p=constt. Of time
If τ(torque)0,L=constt of time.

 

[kuruman]

If F_external=0,p=constt. Of time
If τ(torque)0,L=constt of time.

Very good. So now you need to answer the following two questions
(a) Is there a net force acting on the system? If yes, linear momentum is not conserved.
(b) Is there a net torque about the pivot acting on the system? If yes angular momentum is not conserved.
Once you have sorted out what is and what is not conserved, you can go back and figure out which of the four statements are NOT true.

 

[Apashanka]

(a) Is there a net force acting on the system? If yes, linear momentum is not conserved.

No external force is acting ,p is conserved.
No torque is acting as no external force is acting .
So both p and L are conserved.

 

[kuruman]

No external force is acting ,p is conserved.

Why not? Is gravity not an external force? Is the system hanging in mid air? Read the problem.

No torque is acting as no external force is acting .

You can have a net torque without having a net force. When you turn on an electric drill, there is a net torque that changes the angular momentum of the drill bit but the net force is sero because the center of mass of the drill does not accelerate.