# Momentum concept problem

1. Dec 25, 2012

### VHAHAHA

i sometimes don't know why momentum is conserved is these cases(for both linear and angular), i know that for momentum to conserve , external net force(linear) or external net torque should be zero
can someone plz help me with the following two condition??
Case1
A bomb is projected to the mid air, and then exploded in the mid air and two fragments are formed
we have
(Mass of the bomb)( velocity before explosion) = (Mass of fragment 1 )( V of F1) + (M of fragment 2 ) ( V of F2)
Why?? i think there is a external force acting on the bomb and it is Mg ? after explosion there are also m1g and m2g acting on the fragments respectively? why conserved? the net force is not zero

Case2
In fact it is a question that was asked in this forum before, but i dun understand the concept
Two balls of mass 2.26 kg are attached to the ends of a thin rod of negligible mass and length 72 cm. The rod is free to rotate without friction about a horizontal axis through its center. A putty wad of mass 145 g drops onto one of the balls, with a speed 2.7 m/s, and sticks to it. What is the angular speed of the system just after the putty wad hits?

Why the angular momentum conserved just b4 and after collision ? there is a external non zero net force acting on system that is the weight of the putty wad?

i know how to do these question but i dun know the concept, can anyone help

2. Dec 26, 2012

### haruspex

Change in momentum due to a force is the integral of the force wrt time. Immediately after the explosion, no time has elapsed, so gravity has not had time to change the momentum.

3. Dec 26, 2012

### Andrew Mason

You would be correct if you were being asked what the momentum of the bomb fragments was some time after the explosion. But if the question is just asking you for the total momentum immediately before and immediately after the explosion, total momentum would not change. The change in momentum from gravity is Force x time through which the force acts. If that time interval is arbitrarily small enough, gravity does not add significant momentum.

What is the angular momentum of the putty wad relative to the axis of rotation immediately before the wad strikes the ball? (hint: you have to know the angle of its velocity to the rod at the time of impact). Add that angular momentum to the angular momentum of the rod/ball system. That is the total angular momentum immediately before the collision. Assume the impact occurs over a very short time interval. What is the angular momentum immediately after the impact. (remember again, if you make the time interval small enough, the torque due to gravity will not add significant angular momentum $\Delta L = \tau\Delta t$).

AM

Last edited: Dec 26, 2012
4. Dec 26, 2012

### VHAHAHA

i see
it means that the time for ch is very short so that effect of gravity can be neglected
right ? thx

5. Dec 26, 2012

### Fightfish

This is what we call the "impulse approximation". The collision forces act over a very short interval - and so their magnitudes are very very large, making external forces such as gravity negligible.