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Inertia is the tendency for moving object to continue to move at constant velocity.

My book says

In order to initiate motion in an object, inertia must be overcome to start the movement.

But that is because there is a force pushing it. I don't think the definition of inertia takes in to consideration any forcing acting on the object during the entire course of its movement. My understanding is the force consumed to "overcome" inertia is basically the force required to accelerate it to a certain speed.

Also can inertia be simply described by ${\bf F}=m{\bf a}$?

Like when I jump with my legs, my legs are overcoming the inertia/weight of my body including my legs themselves and produces an acceleration?

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closed as unclear what you're asking by ja72, stafusa, Jon Custer, Daniel Griscom, M. Enns Nov 4 '17 at 14:32

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    $\begingroup$ Sounds as if you need a new book Doeser. Inertia is resistance to change in motion. You don't "overcome" it. Even when you've got something moving, it still exerts resistance to change in motion. $\endgroup$ – John Duffield Jul 21 '15 at 18:09
  • $\begingroup$ What is the confusion? The sum of all forces equals the rate of change of momentum, which is equal to mass times acceleration of the center of mass. $\endgroup$ – ja72 Oct 31 '17 at 17:30
  • $\begingroup$ Incidentally, the title (v3) sounds like something out of Aristotelian mechanics. $\endgroup$ – Qmechanic Nov 1 '17 at 12:22
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Inertia is just another name for mass: it is the property that if you kick a rock so that it makes a certain arc, it will take twice the force to make that arc when you kick two rocks glued together (twice the mass, twice the inertia).

You do not really "overcome it" in the sense of finally being victorious and never having to care about it again. In particular, when you want to stop the thing, you have to also use twice the force -- or if it's in motion and you want it to move faster, the same is true.

You can see this if you live near a place with boats: find a big boat, the bigger the better, that's in the water but tethered to the shore. Pull on the rope that holds it to the shore, and marvel as your puny little human arms move this boat that's much larger than you are. It won't be a large effect at first, and you might struggle if the wind's at your back, but otherwise you can generally do it. Floating objects do not obey our "static friction" rules that keep a pencil on your desk from slipping off of it, so they immediately respond to your force, which produces small accelerations that can eventually build up to a large effect.

So the better way to think about it is: when you try to jump with your legs, you provide a lot of force to your body, which accelerates it upward, giving it an upward velocity. If the force is high enough, you pass the point where you are "just on your tippie-toes" and go airborne, so your legs leave the ground. (Of course, the force of your weight then starts to act on this upward velocity, turning it back to the ground.)

Mass enters the picture in two ways: if your leg muscles are more massive, you can provide a larger force, generally raising the height you can jump; but if any other part of you is more massive, it generally lowers the height you can jump, because it lowers the effect of the acceleration.

Don't think of mass as a barrier to overcome, think of it as a constant penalty to any change in motion. If you swing a bat at a baseball you're going to knock the baseball flying; if you swing a bat at a car you'll maybe move the car a little, but that's it. If a baseball is flying 30mph through the air, the effects of the air on it are going to be much more noticeable than the effects of the air on a car flying through the air at the same speed. Finally if you get hit by a 30mph baseball you'll probably survive (except for a couple of very particular ways it might hit you) and the baseball will stop; but getting hit by a 30mph car, you'll probably die (xcept for a couple of very particular ways it might hit you) and you'll go flying.

In summary: (1) You have to pay larger forces if you want to move larger objects: that is what's called inertia. (2) Inertia isn't a barrier to be overcome; it is always there. )(3) The property which measures this "largeness" or "inertia" properly is called mass. (4) We are very lucky that everything falls with the same acceleration, which give us "scales" that we can use to accurately measure mass via measuring weight. But they are different phenomena, as you have the same mass on the Moon, but you weigh a lot less and can therefore jump a lot higher.

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  • $\begingroup$ Don't all these happen in ideal conditions? $\endgroup$ – most venerable sir Jul 22 '15 at 0:04
  • $\begingroup$ When you mean acceleration that can build to a larger effect, do you mean only velocity increase but acceleration is constant? $\endgroup$ – most venerable sir Jul 22 '15 at 0:07
  • $\begingroup$ (1) It's not just ideal conditions: Newton is providing you a way to think about the world. We call that, in science, a scientific theory: you model the world within the framework. So these things are always true, not just in ideal conditions -- you use the theory to model the world, and when the models get too complicated we'll switch to a theory which does more of the legwork for us. (2) I just mean that the small force eventually can move a big thing a long distance, by increasing the velocity and letting that act on the position. $\endgroup$ – CR Drost Jul 22 '15 at 2:29

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