# System of particles, impulse and conservation of angular momentum

Spector989
Homework Statement:
A uniform rod of length 6 a and mass 8 m lies on a smooth horizontal table. Two particles of masses m and 2 m moving in the same horizontal plane with speed 2 v and v respectively, strike the rod and stick to the rod after collision as shown in the figure. The velocity of centre of mass and angular velocity about centre of mass just after collision are respectively. ( Diagram is provided)
Relevant Equations:
Integration(F.rdt)= impulse
I1.W1 = I2W2 [ I = Moment of inertia , W = angular speed ]
M1V1 = M2V2
So i was able to solve the angular velocity part but i don't know how to find the velocity of centre of mass . For the first part i simply conserved momentum about COM because if i consider the particles as a part of the same system as rod the collision are internal forces . I am mainly confused as to how to solve it mathematically and properly . Thanks

#### Attachments

• 20221126_091649.jpg
44.1 KB · Views: 6

Homework Helper
Gold Member
2022 Award
i don't know how to find the velocity of centre of mass

Is the linear momentum conserved?
If it is, what can you say about the motion of the center of mass for the entire system?

Homework Helper
Gold Member
2022 Award
For the first part i simply conserved momentum about COM
?
Do you mean for the second part you used conservation of angular momentum about CoM?
What did you get?

Spector989
?
Do you mean for the second part you used conservation of angular momentum about CoM?
What did you get?
Mb , for the second part i conserved angular momentum , i got W = v/5a

• Shreya
Spector989
Is the linear momentum conserved?
If it is, what can you say about the motion of the center of mass for the entire system?
Well external force=0 so velocity of COM = 0 ?

Shreya
Well external force=0 so velocity of COM = 0 ?
Conservation of linear momentum says that if external force is 0, the momentum is conserved (not that its neccessarily 0). Why dont you try to write the conservation of linear momentum equation & see what you come up with?

• malawi_glenn
Spector989
Conservation of linear momentum says that if external force is 0, the momentum is conserved (not that its neccessarily 0). Why dont you try to write the conservation of linear momentum equation & see what you come up with?
What i meant to say is that as the net external force is zero, the velocity of Centre of mass will be conserved which was zero initially so the centre of mass will stay at rest

• Shreya
Spector989
What i meant to say is that as the net external force is zero, the velocity of Centre of mass will be conserved which was zero initially so the centre of mass will stay at rest, or... maybe not , now that i think about it . Imma try something else and check back

Shreya
Your idea the CM will stay at rest is correct, but only writing the equation will help you understand why. And dont forget to include the other 2 (moving) particles in your system.

• Spector989
Spector989
Your idea the CM will stay at rest is correct, but only writing the equation will help you understand why. And dont forget to include the other 2 (moving) particles in your system.
Yeah that is what i am trying , thanks for clearing it :)

• Shreya
Spector989
Is it alright if i post a similar question in this thread or do i create a new one , the question is pretty same but instead of colliding body simply impulse is imparted to an end point

Shreya

• Spector989
Shreya
Conservation of angular momentum can only be applied if external torque is 0. Do you see why here it is not so?

Spector989
Conservation of angular momentum can only be applied if external torque is 0. Do you see why here it is not so?
But external torque about the point of application of impulse will be zero , right ?

Spector989
We can converse angular momentum if external torque about any axis is zero , about that axis . ( by i mean:- axis ~ axis of rotation )

Homework Helper
Gold Member
2022 Award
But external torque about the point of application of impulse will be zero , right ?
There are two points where an impulse is applied. You are asked for the AM about the centre of mass, so in any case you should be looking at AM about the centre of mass.

Shreya
hmm, alright...Impulse here means a change in angular momentum. If you look at the right ball from your axis, it experiences an impulse, aka a change in angular momentum. Try calculating that.

• Spector989
Spector989
There are two points where an impulse is applied. You are asked for the AM about the centre of mass, so in any case you should be looking at AM about the centre of mass.
Is it a given that it is about the com when it simply says find Angular velocity of system

Shreya
There are two points where an impulse is applied. You are asked for the AM about the centre of mass, so in any case you should be looking at AM about the centre of mass.
wouldnt it be the same for both axes ?

Spector989
wouldnt it be the same for both axes ?
Yeah mb Angular momentum will be different but angular velocity will be same

Spector989
hmm, alright...Impulse here means a change in angular momentum. If you look at the right ball from your axis, it experiences an impulse, aka a change in angular momentum. Try calculating that.
Solved it , i got confused for no reason. Well thanks a lot for all the help :)

Homework Helper
Gold Member
2022 Award
Is it a given that it is about the com when it simply says find Angular velocity of system
I missed that we've moved on to a new question. The angular velocity is the same about any point on the body. In this case, there's no advantage in considering the AM about the CoM.

• Spector989
• 