Momentum is a measurement of mass in motion. Any object that is moving has momentum. As defined by Newton, the momentum of an object (p) is the product of the mass (m) and velocity (v) of the object. In physics, the momentum of an object is equal to the mass times the velocity.
Usually, momentum is abbreviated using the letter “p” making the equation looks like:
where p is the momentum, m is the mass and v is the velocity
From this equation, we can see that the velocity of the object and the mass have an equal impact on the amount of momentum.
We have more momentum when we are running than when we are walking. Similarly, if a car and bicycle are traveling down the street at the same velocity, the car will have more momentum (due to its higher mass).
Momentum can be considered the power when an object is moving that is to say how much force it can have on another object. For example, a bowling ball (large mass) pushed very slowly (low velocity) can hit a glass door and not break it, while a baseball (small mass) can be thrown fast (high velocity) and break the same window. The baseball has a larger momentum than the bowling ball. Because momentum is the product of the mass and the velocity affect the momentum of an object. As shown, an object with a large mass and low velocity can have the same momentum as an object with a small mass and large velocity. A bullet is another example where the momentum is very high, due to the extraordinary velocity.
Momentum is a vector quantity. A vector quantity is a quantity that is fully described by both magnitude and direction. To fully describe the momentum of a 5 kg bowling ball moving westward at 2m/s, we must include information about both the magnitude and the direction of the bowling ball. It is not enough to say that the ball has 10 kg m/s of momentum; the momentum of the ball is not fully described until information about its direction is given. The direction of the momentum vector is the same as the direction of the velocity of the ball. The direction of the velocity vector is the same as the direction that an object is moving. If the bowling ball is moving westward, then its momentum can be fully described by saying that it is 10 kg m/s westward. As a vector quantity, the momentum of an object is fully described by both magnitude and direction. The direction of momentum is shown by an arrow or vector.
Unit of momentum is kg m/s (kilogram meter per second) or N s (Newton second).
Impulse – Impulse is the change in momentum caused by a new force; this force will increase or decrease the momentum depending on the direction of the force; towards or away from the object that was moving before. If the new force (N) is going in the direction of the momentum of the object (x), the momentum of x will increase; therefore if N is going towards object x in the opposite direction, x will slow down and its momentum will decrease.
In understanding the conservation of momentum, the direction of the momentum is important. Momentum in a system is added up using vector addition. Under the rules of vector addition, adding a certain amount of momentum together with the same amount of momentum going in the opposite direction gives a total momentum of zero. For instance, when a gun is fired, a small mass (the bullet) moves at a high speed in one direction. A larger mass (the gun) moves in the opposite direction at a much slower speed. The recoil of a gun is because of the conservation of momentum. The gun moves back at a lower velocity than the bullet because of its greater mass. The momentum of the bullet and the momentum of the gun are exactly equal in size but opposite in direction. Using vector addition to add the momentum of the bullet to the momentum of the gun (equal in size but opposite in direction) gives a total system momentum of zero. The momentum of the gun bullet system has been conserved.
When two objects bump into each other, it is called a collision. In physics, a collision doesn’t have to involve an accident (like two cars crashing into each other), but can be any event where two or more moving objects exert forces on each other for a short period of time.
There are two types of collision – elastic and inelastic
An elastic collision is one in which no kinetic energy is lost. The elastic collision occurs when the two objects "bounce" apart when they collide.
An inelastic collision is one in which some of the kinetic energy of the colliding bodies is lost. This is because the energy is converted into another type of energy like heat or sound. Inelastic collisions occur when two objects collide and do not bounce away from each other.
Examples:
An important theory in physics is the law of conservation of momentum. This law describes what happens to momentum when two objects collide. The law states that when two objects collide in a closed system, the total momentum of the two objects before the collision is the same as the total momentum of the two objects after the collision. The momentum of each object may change, but the total momentum must remain the same.
For example, if a red ball with a mass of 10 kg is travelling east at a speed of 5m/s and collides with a blue ball with a mass of 20 kg travelling west at a speed of 10 m/s, what is the result?
First we identify the momentum of each ball before the collision:
Red ball = 10 kg * 5 m/s = 50 kg m/s east
Blue ball = 20 kg * 10 m/s = 200 kg m/s west
The resulting momentum will be both balls = 150 kg m/s west
Note: An object standing still has a momentum of 0 kg m/s.
The momentum that we discussed above is largely Linear momentum. It is consistent with our understanding of momentum – a large, fast-moving object has greater momentum than a smaller, slower object. Linear momentum is expressed as p = mv
According to the Principle of Conservation of Linear Momentum, in the absence of external forces, the total momentum of a system does not change. The momentum of the individual components can, and usually do, change but the total momentum of the system remains constant.
But what about objects moving in a circle? It turns out that we can't quite imagine angular momentum in the same way. Angular momentum is the momentum of an object that is either rotating or in a circular motion and is equal to the product of the moment of inertia and the angular velocity. Angular momentum is measured in kilogram meters squared per second.
A rotating body has inertia associated with it called the moment of inertia. The moment of inertia is like mass in linear momentum since it is the resistance to change in rotational speed when a torque (rotational equivalent to force) is applied.
The moment of inertia depends on:
Angular momentum is expressed as L = Iω. This equation is an analog to the definition of linear momentum as p = mv. Units for linear momentum are kg m/s while units for angular momentum are kg m2/s. As we would expect, an object that has a large moment of inertia I, such as Earth, has a very large angular momentum. An object that has a large angular velocity ω, such as a centrifuge, also has a rather large angular momentum.
Conservation of angular momentum explains many phenomena. The total angular momentum of a system remains unchanged if no external torque acts on it. The rotational speed can change simply by changing the moment of inertia.
An example of conservation of angular momentum is when an ice skater is executing a spin. The net torque on her is very close to zero, because there is relatively little friction between her skates and the ice, and because the friction is exerted very close to the pivot point. Consequently, she can spin for quite some time. She can do something else, too. She can increase her rate of spin by pulling her arms and legs in. Why does pulling her arms and legs increase her rate of spin? The answer is that her angular momentum is constant because of the net torque on her negligibly small. Her rate of spin increases greatly when she pulls in her arms, decreasing her moment of inertia. The work she does to pull in her arms results in an increase in rotational kinetic energy.
There are several other examples of objects that increase their rate of spin because something reduced their moment of inertia. Tornadoes are one example. Storm systems that create tornadoes are slowly rotating. When the radius of rotation narrows, even in a local region, angular velocity increases, sometimes to the furious level of a tornado. Earth is another example. Our planet was born from a huge cloud of gas and dust, the rotation of which came from turbulence in an even larger cloud. Gravitational forces caused the cloud to contract, and the rotation rate increased as a result.
In the case of human motion, one would not expect angular momentum to be conserved when a body interacts with the environment as its foot pushes off the ground. Astronauts floating in space have no angular momentum relative to the inside of the ship if they are motionless. Their bodies will continue to have this zero value no matter how they twist about as long as they do not give themselves a push off the side of the vessel.
