Physics: Momentum

[masterMood]

Hi all,
I just wanted some clarification on momentum.

I know how to work the equations and solve problems with momentum but frankly I don't know what exactly momentum is!

Like I understand velocity intuitively and I understand acceleration intuitively but what is momentum intuitively? Force is intuitive because I think of how much acceleration an object can go through for isntance.

Is momentum where when you have more of it, the object starts to build speed a lot faster or something?

Furthermore what is impulse intuitively?

As far as I gather, momentum allows us to figure out certain variables like velocity or Force

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[Vihsadas]

Well the reason that momentum is so important is because it is a conserved quantity in newtonian motion dynamics. In fact, if we are only considering motion and collisions, energy is often not conserved. So this is why momentum is important.

The way you can think of momentum intuitively is to realize that the quantity "momentum" describes what happens to the motion of masses after two masses interact. Try this:
You have a very big mass in space. If you hit that very big mass with a much smaller mass moving very fast, and all of its energy is transferred, you wouldn't expect the bigger mass to continue at the same speed as the smaller mass. You would intuitively expect that the larger mass will begin to move very slowly. This is the heart of the intuition of momentum. A bigger mass requires more energy to accelerate it to velocity 'v', than a smaller mass. So the quantity 'momentum' is used to describe how masses will interact.

Impulse is defined as Force*t. When you normally do force problems with say two billiard balls colliding, you assume instantaneous energy transfer. In this scenario, the momentum is transfered instantaneously to the second pool ball.
In reality there are many scenarios where a force will be applied over time to another object. Think of standing behind a stalled car and pushing it down the road. When forces are applied over time, you have 'impulse'. Now, here's the cool thing:
With normal momentum problems you assume the momentum and energy is transferred instantaneously. With impulse problems you do not! This is why with an impulse problem, a small mass over a long period of time can end up imparting a large amount of momentum on a much bigger mass.
For your own edification, do a dimensional analysis of Force*t and see what you come up with!
Think, now, about how your original intuition of what 'momentum' is and how that relates to 'impulse'.

 

[TheBoondocks]

Well the reason that momentum is so important is because it is a conserved quantity in newtonian motion dynamics. In fact, if we are only considering motion and collisions, energy is often not conserved. So this is why momentum is important.

The way you can think of momentum intuitively is to realize that the quantity "momentum" describes what happens to the motion of masses after two masses interact. Try this:
You have a very big mass in space. If you hit that very big mass with a much smaller mass moving very fast, and all of its energy is transferred, you wouldn't expect the bigger mass to continue at the same speed as the smaller mass. You would intuitively expect that the larger mass will begin to move very slowly. This is the heart of the intuition of momentum. A bigger mass requires more energy to accelerate it to velocity 'v', than a smaller mass. So the quantity 'momentum' is used to describe how masses will interact.

Impulse is defined as Force*t. When you normally do force problems with say two billiard balls colliding, you assume instantaneous energy transfer. In this scenario, the momentum is transfered instantaneously to the second pool ball.
In reality there are many scenarios where a force will be applied over time to another object. Think of standing behind a stalled car and pushing it down the road. When forces are applied over time, you have 'impulse'. Now, here's the cool thing:
With normal momentum problems you assume the momentum and energy is transferred instantaneously. With impulse problems you do not! This is why with an impulse problem, a small mass over a long period of time can end up imparting a large amount of momentum on a much bigger mass.
For your own edification, do a dimensional analysis of Force*t and see what you come up with!
Think, now, about how your original intuition of what 'momentum' is and how that relates to 'impulse'.

yeah what he said. you rock vihsadas. and i'm sure next year will be much kinder, you just applied too late. but you fixed that problem so i'll look forward to your acceptances.

 

[BerkReviewTeach]

Well the reason that momentum is so important is because it is a conserved quantity in newtonian motion dynamics. In fact, if we are only considering motion and collisions, energy is often not conserved. So this is why momentum is important.

The way you can think of momentum intuitively is to realize that the quantity "momentum" describes what happens to the motion of masses after two masses interact. Try this:
You have a very big mass in space. If you hit that very big mass with a much smaller mass moving very fast, and all of its energy is transferred, you wouldn't expect the bigger mass to continue at the same speed as the smaller mass. You would intuitively expect that the larger mass will begin to move very slowly. This is the heart of the intuition of momentum. A bigger mass requires more energy to accelerate it to velocity 'v', than a smaller mass. So the quantity 'momentum' is used to describe how masses will interact.

Impulse is defined as Force*t. When you normally do force problems with say two billiard balls colliding, you assume instantaneous energy transfer. In this scenario, the momentum is transfered instantaneously to the second pool ball.
In reality there are many scenarios where a force will be applied over time to another object. Think of standing behind a stalled car and pushing it down the road. When forces are applied over time, you have 'impulse'. Now, here's the cool thing:
With normal momentum problems you assume the momentum and energy is transferred instantaneously. With impulse problems you do not! This is why with an impulse problem, a small mass over a long period of time can end up imparting a large amount of momentum on a much bigger mass.
For your own edification, do a dimensional analysis of Force*t and see what you come up with!
Think, now, about how your original intuition of what 'momentum' is and how that relates to 'impulse'.

Excellent post as usual. I just wanted to add a little note that we bring up in lectures: "Momentum, like Nascar, is only interesting when it's transferred!" People only want to see the crashes! Most of what matters with momentum is not the vector associated with a single moving object, but more so the conservation and/or transfer that occurs during a collision or explosion in the absence of an external force.

And Vihsadas ode to impulse is an excellent one. It's the central point in designing cars that are safe during crashes.

 

[ChubbyChaser]

VIhsadas you should just forget medical school and just start your own test prep company. I know I would definitely use it.

 

[Vihsadas]

Haha, thanks guys. What I really want to be teaching is medicine though!

 

[Begaster]

I think Vihs has more or less explained it well. All I want to add is a minor point in intuition.

You understand force, velocity, and acceleration. So you understand that if we apply a force to something moving along a frictionless surface, it will accelerate proportional to its mass (F = ma). When we remove the force, since there is no friction and no counter-forces working on the ball, it will maintain its velocity indefinitely. Intuitively, though, why does it maintain this velocity? Momentum. The momentum it possesses is why it won't just decide to stop. Momentum is the ability for an object to maintain its state of motion. An opposing force is needed to end this momentum. The greater the velocity, the greater the momentum, the more energy you need to slow the object down.

Hope that helps.

 

[masterMood]

I think I get what you guys are saying. See I understand that the more velocity that you have, the greater the momentum is (or if the mass is greater then the momentum is greater too), but it's hard to "feel" what momentum deep down really is.

Like mass, acceleration, velocity are things that are tangible (mass - you know how much of something there is, velocity is the change in displacement over time makes sense, work - it's the amount of force done over a certain distance, Newton/meter - is the amount of force done per unit length makes sense).

But momentum is just (kg) m/s. Where is the intuition in that? I guess I'm thinking that an object stays in motion because of an objects resistance to change i.e. due to its mass or its inertia (which satisfies one criteria of momentum MASS) and lack of force (which means constant velocity even if its 0 m/s or 200 m/s)

Maybe I'm just overthinking something that is unnnecessary/approachign philosophical lol...

 

[masterMood]

This is the intuition that I speak of:

"ny moving body is said to possess momentum.
An object which is at rest has no momentum.

There is a ball and stone on the ground. Since they are at rest they don't have momentum. To make it have momentum one must make it move.

Naturally we kick them to gain momentum {motion}.
We will kick the ball but not the stone. Why?
A boy riding a bicycle is coming toward us, of course with some small speed.
If you do want, you will dare to stop him by pushing against the hand bar of the bicycle.
Since the boy was in motion he had momentum. Having stopped him, he has lost his momentum.
A heavily loaded lorry is coming down the slope just starting from rest. You will not dare to stop it by pushing against it, even though it is coming slowly.
A mosquito or a fly is flying toward you. With the palm, you will push aside it.
If a bullet is coming toward you, you will not stop it but will avoid it hitting you.

By analyzing such things in motion, we come to a conclusion that the quantity of motion depends not only on the speed of the object but also on the mass of the object.

To stop an object in motion we have to impart equal and opposite momentum to that object and that depends on the product of the mass and speed of that object."

 

[Vihsadas]

That seems like a valid way to internalize the concept of momentum. I think you've got it.

 

[tncekm]

I just think of playing football with three guys of different weights running the same speed.

50kg person runs at me at 5m/s and I block him, he bounces off, and laugh because he could hardly make me budge because his inertia is less than mine and the momentum he imparted on my initially momentum-less body wasn't enough to make me move significantly.

100kg person runs at me at 5m/s and I block him, we both tumble, and I scratch my head because he has equal inertia to mine, and the momentum he imparted on my initially momentum-less body gave me a rocking.

200kg person runs at me at 5m/s and I jump out of the way because his inertia is much greater than mine and his momentum would have sent my initially momentum-less body flying through the air.

All three move the same speed, but carry different momentums, and those different momentums would have different effects on how our collisions ended up.