# Momentum

"Momentum; A function of mass and velocity; is conserved [. . .] In layman's terms: Speedy-thing goes in, Speedy-thing comes out." -GLaDOS

# Momentum

Momentum explains many things that go on in physics. It is a vector quantity, so it has direction and magnitude, which is a very important aspect when it comes to momentum calculations. The formula for calculating momentum is mass times velocity. Momentum is represented by p, so p=mv. Momentum is a force and a conserved quality. Therefore, the amount of momentum of a system stays the same unless an outside force acts on it. The more momentum a system or object has, the more difficult it is to stop. When an outside force is acting upon a system for a given amount of time, the object's velocity is changed, and therefore, it's momentum is changed. An example of this situation can be seen in football. In football, the defensive players apply a force for a given amount of time to stop the momentum of the offensive player who has the ball. Another example would be when you're driving a car. As you bring your car to a halt when approaching a stop sign or stoplight, the brakes serve to apply a force to the car for a given amount of time to change the car's momentum. An object with momentum can be stopped if a force is applied against it for a given amount of time. [5][1]

## Vocabulary

• Momentum - Quantity of motion an object has; momentum = mass times velocity (p=mv)
• Velocity - Speed with a direction
• Impulse - A force so communicated as to produce motion suddenly.
• Inertia - The resistance an object of mass has to not change velocity or direction.
• Acceleration - The change in velocity with time.
• Kinetic energy - The energy of a body or a system with respect to the motion of the body or of the particles in the system.
• Collision - An encounter between particles resulting in an exchange or transformation of energy.
• Elastic collision - A collision where the objects do not stick together and kinetic energy and momentum are conserved.
• Inelastic collision - A collision where the objects do not stick together and kinetic energy is not conserved while momentum is.
• Law of Conservation of Momentum - In the absence of external forces, the total momentum of the system is conserved.
• Vector - A quantity that has magnitude and direction and that is commonly represented by a directed line segment whose length represents the magnitude and whose orientation in space represents the direction.
• Force - A push that affects the speed or direction of an object or system.

### Impulse Changes in Momentum

A force applied over time is an impulse, which is also change in momentum. When two objects collide, there is an impulse. If the time of a collision can be measured, then the average force of impact can be calculated. The greater the impulse applied to something is, the greater the change in momentum will be. Another important thing that changes momentum is time. The amount of time a force acts on an object affects how great the change in the object’s momentum will be. The impulse applied by force on a system equals the change in momentum of the system. That is, for the most part, Newton’s Second Law. This has also been called the Impulse-Momentum form of Newton’s Second Law. The impulse-momentum relationship helps us to better understand the analysis of a variety of situations in which momentum is changed. Another example of this would be determining the give of a surface and difference in impact time.
 Image Courtesy of Sat51.net

The longer a force accelerates an object, the more momentum the object will have. Consider riding a bike. If you pedal really hard for one seconds you will go a certain distance, but if you pedal extremely lightly for 20 seconds you will go a longer distance; however, the impulse will be less because the time in which the force is applied will be greater.

### Bouncing and Collisions

Impulses are greater when objects bounce. The impulse required to bring an object to a stop and then to throw it back again is greater than the impulse required merely to bring the object to a stop. It requires greater impulse to catch an object and throw it back up than to merely catch it. An example of this would be a waterwheel used in the California Gold Rush. The waterwheels were not very effective, but a man named Lester A. Pelton discovered that the problem was with the the flat paddles. He designed a paddle with a curve-shape that caused the incoming water to make a U-turn upon impact with the paddle. This relates to momentum because as the water "bounced," the impulse exerted on the waterwheel was increased.

There are 3 different types of collisions when it comes to momentum: elastic, perfectly inelastic, and inelastic. An elastic collision is when two objects collide and immediately bounce apart and go opposite directions. In this type of collision both momentum and kinetic energy are conserved. An inelastic collision occurs when two objects collide and momentum is conserved, but kinetic energy isn't. An example of this would be hitting a golf ball with a club because the ball is deformed momentarily when it is hit. Last, a perfectly inelastic collision is one where two objects collide and stick together. This kind of collision is very rare, but an example would be playdough or silly puddy.

### Conservation of Momentum

The idea that momentum is conserved when no external force acts is elevated to a central law of mechanics. It is known as the Law of Conservation of Momentum. This states that in the absence of an external force, the momentum of a system remains unchanged. Conservation of energy and mass don't convey to any of the three dimensions of space because they're scalars. An example of this would be two cars colliding. The net momentum of the system before and after the event will remain the same. To better understand the
 Image Courtesy of Sparknotes.com
conservation of momentum, you must first understand the concept of momentum. Momentum has both direction and magnitude. Similar to that of velocity and force, momentum can be canceled. If there is no net force or impulse acting on a system, the momentum will not change. Another example of the Conservation of Momentum would be a little kid playing in a wagon. If he pushes himself forward to move, the wagon would push him back because it made an equal and opposite reaction on the kid resulting in no movement forward due to it being a closed system. Something can move while not changing the total amount of momentum. If we call a forward movement positive and a backward movement negative, then we can say that one of a system's parts can gain a negative movement while another gets the positive one. It is like a cannon shooting a cannon ball, it takes a lot of force to get that cannon ball going, but there is hardly a negative force acting on it. That negative force acts onto the actual cannon while the positive one pushes the cannon ball to the enemy. That cannon will be pushed back with equal force that it took to get that ball going. [3]

## Presentations

References

1. The Physics Classroom
2. Highlights Kids
3.Light and Matter
4.regentprep.org
5.Hyperphysics