# Conceptual Question about Conservation of Momentum

1. May 11, 2012

Hi,

I just want to understand this concept a bit better. The law states that momentum is conserved when there is no external force acting on the system.

Now consider this situation where two cars of equal mass and moving at equal speed collide head-on to come to rest.

Would the momentum be conserved? Looking at the situation, there is friction acting on the cars so does that mean momentum is not conserved?

Similarly for this situation: a bicycle rider ceases to pedal and her bicycle coasts along the path until it comes to rest. Is momentum not conserved as well due to friction?

Many thanks.

2. May 11, 2012

### A.T.

Yes it is zero all the time. Momentum is a vector, and the conserved net momentum is a vector sum.

Friction with the ground? That is an external force, unless you include the entire Earth in your momentum balance. In a symmetrical cases however, where the cars are identical and have the same rolling resistance the net external force is zero too, because forces are vectors too.

3. May 11, 2012

### tiny-tim

momentum is conserved in any direction in which there is no external force

(And angular momentum is conserved about any axis about which there is no external torque)

in a collision, momentum is conserved in any direction in which there is no external impulse

(and in a collision, angular momentum is conserved in any direction in which there is no external impulsive torque)

friction (unlike say, a step or a barrier) is not impulsive, so you use it before and after the collision, but you ignore it for the collision itself!
if we ignore the rolling resistance (the continual deformation of the tyre where it meets the road), and the frictional torque on the axle, then there are no external forces or torques, and the bike goes on for ever

4. May 11, 2012

However, given the situation that the bicycle does eventually go to REST as stated in the question, how can it go on forever? Would the momentum be conserved or not if the bicycle eventually goes to rest?

5. May 11, 2012

### Infinitum

There is resistance due to the Earth, and also the frictional torque on the axle(as Tiny-tim said), and these act for a long duration, unlike in collisions. Meaning that there is external impulsive force. So no conservation of momentum.

6. May 11, 2012

### tiny-tim

yes (except, not impulsive)

7. May 13, 2012

### joker94

hi,i have the similar problem...if i include the earth in my system.EARTH HAS ZERO MOMENTUM before and after colision of car right???? then acc to conservation of momentum MV+MV=0(WHERE M IS MASS OF CAR AND V IS VELOCITY OF CARS) then V=0?????

8. May 13, 2012

### Michael C

If you include the Earth in your system, momentum is conserved: the change in momentum of the car is equal and opposite to the change in momentum of the Earth. It's just that nobody will notice the change in momentum of the Earth. Since the Earth is so massive, the change in its velocity will be much too small to be measured.