Conservation of Angular Momentum in a Three Mass System

AI Thread Summary
The discussion focuses on the conservation of angular momentum in a three-mass system where two masses are connected by a rigid rod and a third mass collides with one of them. Before the collision, the angular momentum is calculated using the moment of inertia (I) and the initial angular velocity (w). After the collision, the new angular momentum (L') must be recalculated using the new moment of inertia (I') and the new angular velocity (w'). The center of mass (CM) of the system shifts after the collision, necessitating careful recalculation of I. The conservation of angular momentum principle remains applicable throughout the process.
neelakash
Messages
491
Reaction score
1

Homework Statement



Two masses M each are connected by a rigid rod of negligible mass having length a.The CM of the system is stationary in a gravity free space and the system rotates about the CM. with angular velocity w.One of the rotating masses strikes a third stationary ball of mass M which sticks to it.What is the angular momentum of the three mass system before and after collision?

Homework Equations



The Attempt at a Solution



For the collision conservation of linear momentum will be applicable.
Mv=2Mv' or,v'=v/2=wa/4. From this w' can be calculated.

Prior collision,L=Iw where I is the MI of the two mass system.

After collision, L'=I'w'

Please check if I am correct.
 
Physics news on Phys.org
the system will rotate about new center of mass. Check for the position of new center of mass!
 
So,we are to be careful to calculate I for the second time.
Second time, CM will be a/3 rd distance away from the mass 2M.Accordingly,I will change.

But angular velocity would be same as w'.Right?
 
There will be no linear momentum...
angular momentum will be conserved...
CM will change the position...
And if one wants to find w',one has to find I' carefully.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

How Does Angular Momentum Conservation Affect Asteroid Collision Dynamics?
7
Replies
335
Views
14K
Angular Momentum- Conserved or not?
Replies
17
Views
407
Angular momentum for a bullet and a rod attached to a ceiling
Replies
17
Views
1K
Collision of a bullet on a rod-string system: query
2
Replies
71
Views
2K
System of particles, impulse and conservation of angular momentum
Replies
23
Views
2K
Problem in understanding angular momentum of a rigid body
Replies
10
Views
2K
Find velocities when a mass leaves a system of a rod with two masses
Replies
10
Views
2K
Which system to apply conservation of momentum to?
Replies
2
Views
2K
Angular and Linear Momentum Problem
Replies
18
Views
3K
Ambiguous question on momentum and how it works...
Replies
13
Views
1K

Hot Threads

Recent Insights

Back
Top