what the definition of momentum (1 Viewer)

[wolf7]

i know what the definiyion is that its the prodtct of mass and velocity, but what does the word momentum mean. also can someone explain the law of conversation momentum (refering to space) in simpler terms

 

[insert-username]

Momentum is the inertia, or resistance to change of motion, of a moving object. The more momentum a moving object has, the harder it is to change its motion through the application of an external force.


I_F

 

[Xayma]

Momentum is the inertia, or resistance to change of motion, of a moving object. The more momentum a moving object has, the harder it is to change its motion through the application of an external force.


I_F

Thats mass.

 

[insert-username]

If you say so. I'm pretty sure that's what we learnt momentum as though, but I'd have to check to make sure.


I_F

 

[mitsui]

Thats mass.

um .... personally. i think:

mass is a measurement of the amount of "space" that a matter takes up. so it is not a force nor is it an inertia??? o_o

momentum is the product of mass x velocity

if we r to stop an object from movin, a force needs to be applied, ..the amount of force that we need to apply is depend on the momentum of the object

so if an object got higher mass = more force needed, if the object is travelling at higher velocity = more force needed

...
>o>..

 

[Riviet]

Also, momentum can be related directly to Newton's 1st law of motion: an object will remain at rest and continue in it's constant movement if it is not acted upon by an unbalanced external force. If there are no forces acting on the object, (e.g the closest you can get to this is in space where there is a minimal amount of gravity pull from distance objects), then it's momentum will be constant and keep it moving in the same direction at the same speed.

 

[Halfasian89]

Momentum is the inertia, or resistance to change of motion, of a moving object. The more momentum a moving object has, the harder it is to change its motion through the application of an external force.

The fact that this definition includes the word 'inertia' make the definition look misleading, but is essentially true. But i would rather change 'change of motion' to 'change in direction of motion', for if you consider a falling object that has a massive booster behind (looking from earth), and the booster was turned on, the object having momentum wouldn't be neccessarily resisting the contribution force, in fact it would be embracing it, travelling faster than before and thus gaining extra momentum.

Inertia is the tendacy of an object to resist a change in uniform velocity, or motion in a state of rest. This covers change in direction of motion for velocity is a vector quantity, as it is measured as a magnitude and a direction. But it doesn't cover if the change was just a change in speed.

Just a thought, maybe in too deep.

 

[Stan..]

The conservation of momenta comes from 'm' being constant in a closed system. If you want a definition of the term, maybe you should use a dictionary.

 

[angmor]

from what i tried asking from the teacher, he just gave me the defintion of momentum as mass x velocity. nothing more. i dont think for the hsc course we need to know anything deeper than that.

 

[acullen]

What I don't think was mentioned is that momentum is a vector. It is the product of a scalar (mass) and a vector (velocity).

Therefore it is not necessarily the resistance that may be observed that a body exhibits against an external force; but rather, resistance to forces in the opposite direction of the velocity (whether that resistance may be a vector component of a force).

Momentum can also be seen as the effect an object has in a collision with another object. As the sum of momentum of 2 objects colliding is equal to the momentum after the collision in an elastic collision (one whereby energy is not lost in the transfer to heat or sound).

 

[acullen]

The fact that this definition includes the word 'inertia' make the definition look misleading, but is essentially true. But i would rather change 'change of motion' to 'change in direction of motion', for if you consider a falling object that has a massive booster behind (looking from earth), and the booster was turned on, the object having momentum wouldn't be neccessarily resisting the contribution force, in fact it would be embracing it, travelling faster than before and thus gaining extra momentum.

But there is a resistance to that force, inertia is all about an object resisting an external force (basically put as "things like to keep doing what they are doing"); that is why when you accelerate in a car at a fast rate, you will be pushed back into the seat. This is also why the mirror in a friend's car changes its position if he steps on that right pedal a little too hard...

 

[Captain Gh3y]

So who here does two unit maths?
Kinetic energy = 1/2 mv²
Momentum = mv
Mass (intertia) = m
Does that tell you anything?

Anyway, whoever said momentum = intertia is wrong. And mass isn't a measure of how much "space" something takes up (that's the relationship between mass and density) it is the measure of how much matter an object contains.

The more matter something contains, the more 'intertia' it has, and so the more force needs to be imparted on it to make it do something.

F = ma

For a constant force, a heavier object (more m) will experience less acceleration.

Now, whAen a force is applied to an object for some amount of time, t, this is called Impulse,

I = Ft

And, impulse is in fact relevant to this thread because Impulse IS the change of momentum.

I = change in momentum.

This is because momentum, p, is given by mass times velocity,

p = mv

And F = ma, times time = m*a*t, now acceleration is in m/s². so when you multiply that by time, t, you get m/s, which is obviously velocity. Another way of explaining this is that the unit for force, N, is really just kgm/s², compare this to the unit for momentum, kgm/s.

Coming back to momentum, you can see that when a light object and a heavy object are moving at the same speed, we know that the heavy object must have had more force imparted on it (more impulse, I) to get it up to that same speed.

So if two objects are of different mass, but travelling at the same velocity, the heavier object has more momentum, p = mv.

Now, conservation of momentum says that, err, "momentum can't be created or destroyed", I suppose.

Momentum is, as someone pointed out, a vector, so you can use positive or negative signs to indicate direction.

Say you have two objects of the same mass, travelling at the same magnitude of velocity, but in opposite directions toward each other.

Maybe they both weigh one kilogram and are travelling at 5m/s in opposite direction, so the momentum of one object is 5kgm/s and the momentum of the other is -5kgm/s

So the sum of momenta is 0.

Say they collided, we can now say the sum of momenta after the collision must still be 0, so we can use this to predict what will happen when they collide.

In this case, after the collision they'll both be stationary, assuming they remain whole and don't lose any mass.

Or another example, a 20000kg truck is moving at 33m/s in the opposite direction of a car weighing 1000kg travelling at 16m/s.

Momentum of truck = 20000*33 = 660000kgm/s
Momentum of car = 1000*-16 = -16000kgm/s

Sum of momenta before a collision = 644000kgm/s

Therefore, due to conservation of momentum, sum of momenta after collision still = 644000kgm/s

So if we wanted to see what'd happen when they collided, in most questions (this stuff is only in preliminary course anyway) it'll say something like "assume all the momentum was imparted into the car"

So if in fact all the momentum of the collision was imparted into the car, the velocity of the truck will then be 0, meaning the momentum of the truck is now mv =0, so all the 644000kgm/s is conserved in the car.

p = mv = 644000kgm/s, so

v = p/m = 644000/1000 = 644m/s

So we see the car now moving in the direction the truck was first moving, at a healthy 2390.4km/h.

Which sounds odd considering the original speed of the truck was only about 120km/h, but the point here is the factor of mass.


Addressing what everyone said:

insert-username: That's kinda true, because the more momentum something has the more force must be applied in the opposite direction to stop it. But it's also false in that intertia is only the mass, not the velocity component of momentum.

Xayma: You're half right.

Mitsui: Already addressed that mass is not space, space is volume and is related to mass by density. The rest is right.

Riv: That's true. Then you go to Newton's second law as the 2nd half of IU's post indicates.

Halfasian: Sort of. If the object is very heavy, it therefore has a lot of momentum. Now, if a rocket in space is extremely heavy, even if the booster tries to assist it, the booster needs to impart a LOT of force to speed it up at all. It doesn't matter whether it's for or against the same direction, if it's very heavy, then a small boost (small impulse, small force) will not increase velocity much.

This is in fact why no objects can reach light speed, because they just get heavier and so momentum says that trying to speed it up wont' do anything.

Stan: True, but in all prelim physics problems you always assume that mass remains constant throughout the whole problem so this is never an issue.

Acullen: Right. But it still doesn't matter whether the change in force is in the same or opposite direction that the object is already travelling; the higher the mass, the higher the resistance to change for reasons already explained.

Your second post is actually about Newton's third law.

Any questions?

 

[acullen]

Anyway, whoever said momentum = intertia is wrong. And mass isn't a measure of how much "space" something takes up (that's the relationship between mass and density) it is the measure of how much matter an object contains.

Mass is the numerical measure of intertia. In classical mechanics, it can be seen as the concept you mentioned.

Now, whAen a force is applied to an object for some amount of time, t, this is called Impulse,

I = Ft

And, impulse is in fact relevant to this thread because Impulse IS the change of momentum.

I = change in momentum.

This is because momentum, p, is given by mass times velocity,

p = mv

And F = ma, times time = m*a*t, now acceleration is in m/s². so when you multiply that by time, t, you get m/s, which is obviously velocity. Another way of explaining this is that the unit for force, N, is really just kgm/s², compare this to the unit for momentum, kgm/s.

Your description of impulse is very vague. But as you correctly stated, it is the change in momentum with respect to time.

To derive impulse from Newton's second law, we have:
F=m•a
a=∆v/∆t

so F=m•∆v/∆t

Now we have:
F•∆t=m•∆v

As mass is a constant we can obtain
F•∆t=∆(m•v)

As m•v = p (momentum)
F•∆t=∆p

So integrating both sides with respect to time obtains:
∫F•dt=∫p•dt
F•t=I

And Q.E.D. we have our definition of impulse!

Momentum is, as someone pointed out, a vector, so you can use positive or negative signs to indicate direction.

This is so for momentum in a single dimension, however unit vectors are required for describing momentum in 2 or 3 dimensions.

Say they collided, we can now say the sum of momenta after the collision must still be 0, so we can use this to predict what will happen when they collide.

In this case, after the collision they'll both be stationary, assuming they remain whole and don't lose any mass.

There are energy transformations into heat and sound in an inelastic collision (you probably will need to know this for the HSC, I can't remember that far back whether they actually asked that).

Mitsui: Already addressed that mass is not space, space is volume and is related to mass by density. The rest is right.

The relation between mass and density is only due to density being defined in such a way. Mass itself is a fundemental unit (and a basis) of Classical Mechanics.

Halfasian: Sort of. If the object is very heavy, it therefore has a lot of momentum. Now, if a rocket in space is extremely heavy, even if the booster tries to assist it, the booster needs to impart a LOT of force to speed it up at all. It doesn't matter whether it's for or against the same direction, if it's very heavy, then a small boost (small impulse, small force) will not increase velocity much.

This is in fact why no objects can reach light speed, because they just get heavier and so momentum says that trying to speed it up wont' do anything.

I'm not sure how this was brought up, but this is more in part due to energy. However mass does not increase as you approach the speed of light, OBSERVED mass does from an external reference frame. As kinetic energy is defined as E_k=1/2•m•v², as mass approaches ∞, the amount of energy required to accelerate to c also does. As we know, there is a finite amount of matter and energy in the universe, therefore such a feat for an object with a rest mass is impossible.

Acullen: Right. But it still doesn't matter whether the change in force is in the same or opposite direction that the object is already travelling; the higher the mass, the higher the resistance to change for reasons already explained.

My bad for that. I haven't done Classical Mechanics for a while, the Physics portion of my mind is clogged with Modern Physics and Thermodynamics (and I'm sure Systemic Anatomy has also taken over some space). I think what I was thinking about was more about the effect of the summation of momentums with the vector addition of velocities.

Your second post is actually about Newton's third law.

I was talking more so about the effect of changes in velocity of an object in an inertial frame of reference as an example, not using an alternative situation as a definitive explanation.

Now time for bed I think, I have a lecture in under 7 hours...

 

[beabenn]

Well really the conservation of momentum is a spinoff of Newton's 3rd law
It is most applicable in collisions, there was a question (re apollo 13/newton) in last year's hsc paper basically about the conservation of momentum (but some people talked about slingshot effect) *rolls eyes*
Actually, I take that back because I guess you could say the slingshot effect is a direct result of the conservation fo momentum (and thus relate it to the newton quip) but the slingshot effect is actually a direct result of the conservation of angular momentum and that's different...