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Can you define linear momentum?

  1. Dec 13, 2015 #1
    Ok so I learned about linear momentum and its derivative: force; a while ago. I know linear momentum is the product of mass times velocity but it tells me almost nothing. I´ve heard other names for this like quantity of movement or something like that but it still a blurry concept for me. Can you guys please explain it to me? What does it actually describe?
    Thank you tons!
  2. jcsd
  3. Dec 13, 2015 #2


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    It describes how much effort is required to stop something. A bullet travelling at 300m/s and an Ocean Liner travelling at 3cm/s both have a LOT of momentum. A bullet travelling at 3cm/s - not so much.
  4. Dec 13, 2015 #3
    Momentum describes an phenomenon, just as velocity describes how fast a body is moving, and just how mass describes the amount of matter in an object.

    Our intuition tells us that it takes the same amount of force to stop a body that has a mass of 5 kg going 2 m/s as it does to stop a body with a mass of 10 kg going 1 m/s. Therefore, we define what is called momentum that describes this equivalency. Since we know that both an increase in mass and an increase in velocity make a body harder to stop, we can say that this new quantity, momentum, is proportional to the two quantities velocity and mass. This leads to the fact that momentum is simply the product of the two: p = mv.

    We came up with a new quantity to describe a physical concept. So is the same with any other quantity like velocity, force, or mass; quantities are defined by people, and used to describe quantitative aspects of our reality. Momentum in particular has great use only because of the fact that it is conserved in an isolated system.
    Last edited: Dec 13, 2015
  5. Dec 13, 2015 #4
    Thank you for your answers guys. They are incredibly simple. However, (here comes today´s silly question) why is stopping objects in motion important to physics? If a force changes the state of motion or repose in an object, and therefore a force could stop and object, why is momentum what it is and not a force instead? I mean, so far both force and momentum seem to me to describe almost the same thing.
  6. Dec 13, 2015 #5


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    Force is the time rate of change of momentum.
    They differ in the same way as power and energy, or salary and wealth.
  7. Dec 13, 2015 #6
    I'm not sure if you understand calculus, but the relationship between force and momentum is ## \displaystyle F_{net} = \frac{dp}{dt}##. This means that the net force acting on an object is the rate at which momentum changes.

    Imagine an object at rest, and imagine that a constant force is applied. Visualize a static vector arrow on the object, which represents the force. Now, the object begins to accelerate. Once the object has motion, then we can define a momentum vector, which ever increases as long as that constant force is acting on the body. As one can see, force and momentum are different, although their definitions are intertwined.

    You can think of force as the impetus which causes motion, and momentum as a variable that describes the object's state, just as velocity, acceleration, and mass describe an object's state.
    Last edited: Dec 13, 2015
  8. Dec 13, 2015 #7
    Momentum is an important concept not just theoretically but we use it in our lives everyday. Momentum is the reason why we have airbags in our cars instead of metal steel plates. In a car crash, both airbags and metal steel plates will serve well in applying a stopping force on the driver, but clearly airbags are the better choice.

    Momentum is the reason why the strings on tennis or badminton racquets have to be taut in order for the ball or the shuttlecock to fly across the court. Imagine using a racquet that has loose strings. Why won't that work? If momentum and force were the same (which they are clearly not), then there should not be a difference in using tight or loose strings in racquets.
  9. Dec 14, 2015 #8
    Ok, please correct me if I'm wrong. In the case of the airbag, the impact is absorbed during a crash meaning that the driver's momentum decreases over time. If we used a metal plate the driver's momentum would decrease way too fast (and thus killing the guy) ¿is this the difference?
    When it comes ro tennis racquets, I guess loose strings would not transfer momentum efficiently as tight ones would.
    I might not have understood the references here.
  10. Dec 14, 2015 #9
    Yes, you have the general idea. The key in both of the situations I stated was in the time of contact between the two objects. This is a concept known as impulse, or better known as change in momentum. If the time of contact is short, as in the tennis racquet with taut strings, then the impulse is large, which means that the change in momentum of the tennis ball is large. This is what allows the ball the travel far across the court. Of course, the force applied to the ball by the racquet matters as well, but between tight strings vs. loose strings, the key difference is the time of contact.

    Mathematically, this is represented as $$ \Delta P = (m)(\Delta v) = F(\Delta t)$$. Note the dependence on the time of contact as well as the force applied in determining the momentum change. I hope this also shows that momentum and force are NOT the same thing.

    In the situation of the car crash, the airbag increases the time of contact between the driver and the airbag/dashboard, and for a given momentum change (the driver slows down from 60km/h to 0km/h, this corresponds to a momentum change from the equation above), a longer time of contact would reduce the force felt by the driver, hence increasing his chances of survival.
  11. Dec 14, 2015 #10


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    The part important to physics is this:
    Physics is about making quantitative predictions, and having conserved quantities helps a lot.
  12. Dec 14, 2015 #11
    Ok, by isolated You mean the object is not being affected by any other force right?
    If a certain object is stopped with a certain quantity of momentum, is it right to say that the same momentum is required to set it in motion as well?
    Another silly question: is \delta t a time interval in the impulse equation?
    If I graph time and momentum, lets say momentum is a line with a 20 degree angle and when time equals 10 seconds the momentum graph suddenly changes it's angle to 35 degrees, can I say there was an impulse?
    Thank you guys! I'm really understanding this!
  13. Dec 15, 2015 #12


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    Any momentum will set it in motion, though it requires the same magnitude but in the opposite direction to restore the body to its former state of motion.

    ##\Delta t## is typically the duration for which the force F acts on the body; it's the duration of the impulse.

    If momentum vs. time is a horizontal line then the body (of fixed mass, I'll assume) has a constant velocity and a fixed momentum; a sloping line would mean there must be a force continually acting on the body and thus causing its momentum to steadily increase. A change in slope is an indication that the continually-acting force must have changed to a new magnitude.
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