High mass objects can have low momentum when they have low velocities; low mass objects can have high momentum when they have high velocities

According to Newton's second law, an unbalanced force causes a mass to accelerate. Restating Newton's second law in terms of momentum, an impulse causes the velocity of an object with mass to change, therefore causing a change in momentum

Objects transfer their momentum in collisions. The total momentum before the collision is equal to the total momentum after the collision in a closed, isolated system. If one object loses momentum in a collision, then another object must gain that amount of momentum.

There are two types of collisions:

**Elastic collision**- total momentum and total energy is conserved; elastic collisions only occur on the sub-atomic particle level
**Inelastic collision**- total momentum is conserved; real-life collisions are all inelastic

Method of working linear momentum problems:

- Find the initial momentum of each object. Remember that momentum is a vector quantity--object's velocities are positive or negative. The total initial momentum is the sum of all the object's initial momentum.
- Find the final momentum of each object. Remember that momentum is a vector quantity--object's velocities are positive or negative. The total final momentum is the sum of all the object's initial momentum
- Set the total initial momentum equal to the total final momentum.

**Be careful when working conservation of momentum problems! The problems can be algebraically correct, but not be correct according to the law of conservation of physics. Your physics must be correct--not just your algebra!**

Method of working two-dimensional momentum problems:

- When the velocity of the object is at an angle, resolve this resultant velocity into its x- and its y-components. Remember to assign a positive or a negative sign to the components' velocities.
- Conserve the momentum in the x-direction. Find the initial momentum of each object in the x-direction. In other words, only consider the x-component of its velocity. Add the initial momentum of each object to find the total initial momentum. Find the final momentum of each object in the x-direction. In other words, only consider the x-component of its velocity. Add the final momentum of each object to find the total final momentum. Set the total initial momentum in the x-direction equal to the total final momentum in the x-direction.
- Conserve the momentum in the y-direction. Find the initial momentum of each object in the y-direction. In other words, only consider the y-component of its velocity. Add the initial momentum of each object to find the total initial momentum. Find the final momentum of each object in the y-direction. In other words, only consider the y-component of its velocity. Add the final momentum of each object to find the total final momentum. Set the total initial momentum in the x-direction equal to the total final momentum in the y-direction.
- Step two yields the x-component of the desired velocity. Step three yields the y-component of the desired velocity. Use vector addition of the two components to find the resultant velocity of the object.