Why does the gravitional force causes only centripetal acceleration?

[IbrahimMisbah]

why does the gravitational force causes only centripetal acceleration?

Hello, here I was studying the chapter on gravitation on our introductory mechanics course.I know I should ask that this question to my course teacher but he scares me a lot.Moreover, I sometimes don't even understand what he says.
So, I have more or less studied most of mechanics,gravitation being the last chapter.And There is these theoretical stuffs I am just no getting.Your help will really be appreciated.

1)why does the gravitational force cause only centripetal acceleration not linear acceleration ?

2)What keeps the Earth rotate about it's own axis?


Thanks
IMS

 

[SteamKing]

Number 1 is not true. To cause linear acceleration due to gravity, pick up rock. Drop same.

Number 2: See Newton's First Law of Motion.

 

[rcgldr]

1)why does the gravitational force cause only centripetal acceleration not linear acceleration?

For a two body system, this only happens if the objects orbit in a perfectly circual path. Most of the time the path will be elliptical, and there is both centripetal and linear acceleration involved, with maximum speed occurring when the objects are closest to each other, and minimal speed when they are farthest apart.

What keeps the Earth rotate about it's own axis?

The fact that it has angular momentum and there is almost no drag, except for the tidal drag caused by the moon, which is slowing the Earth's rate of rotation by a tiny amount all the time.

 

[Geezer]

Re: Question #1. You're wrong that only the gravitational force causes centripetal acceleration. "Centripetal" means "center-seeking" not "Earth-seeking." For example, you can take a string/rope/cord and rotate it in a horizontal plane (e.g., like a lasso), and there's centripetal acceleration, but it's NOT pointing towards the center of the Earth.

Re: Question #2

The fact that it has angular momentum and there is almost no drag, except for the tidal drag caused by the moon, which is slowing the Earth's rate of rotation by a tiny amount all the time.

This is correct. ^^

 

[Geezer]

1)why does the gravitational force cause only centripetal acceleration not linear acceleration ?

First, you're wrong about the gravitational force only causing centripetal acceleration.

Secondly, when you differentiate a velocity vector--not the magnitude of the velocity, but the vector itself--of an object moving in a non-linearly, you will get a total acceleration that will have two orthogonal components: you'll get the tangential acceleration (which is perhaps what you're thinking of when you talk about "linear acceleration"?) and you'll get a centripetal acceleration, too. The two components together provide the TOTAL acceleration of the object. But if you're dealing with circular motion, you're often most interested in just the radially-directed "centripetal" component.

 

[tiny-tim]

Welcome to PF!

Hi Ibrahim! Welcome to PF!

I think you and your teacher are using different terminology.

To expand slightly on what Geezer says …

by https://www.physicsforums.com/library.php?do=view_item&itemid=27" we usually mean towards the centre of curvature of the path (the orbit), not towards the star …

after all, the star isn't actually at the centre of anything, is it?

We usually use the word "central" not "centripetal" to describe a force (or acceleration) towards a fixed point ("a central force").

(And the reason why the Earth's rotation is the same today as it was yesterday is because of conservation of angular momentum.)

 

[AIR&SPACE]

ttmark,

The so-called "accepted" theory is "accepted" by multitudes of highly qualified groups and individuals. Also, conservation is true for all systems... open and closed. If an object (let's say Earth) has angular momentum and is acted upon by a force (let's say gravity from the moon) then yes, the angular momentum of Earth may be changed. But that energy has to go somewhere. That's part of the "conservation of angular momentum."

Earth's precession that you refer to is caused by the forces (which "act as" torques because of the non-spherical shape of Earth ie. the equatorial bulge). This is called lunisolar precession.

I am interested in your qualifications/references that lead you to believe what you are saying.

 

[AIR&SPACE]

And please don't tell me you're using http://d1002391.mydomainwebhost.com/JOT/Articles/3-3/uwe.pdf"to the Journal of Theoretics as your source.

 

[Geezer]

And please don't tell me you're using http://d1002391.mydomainwebhost.com/JOT/Articles/3-3/uwe.pdf"to the Journal of Theoretics as your source.

Wow. That's some compelling research there^^. The author even listed his encyclopedia as a reference! And the lack of math...well, the math can't be wrong if it doesn't exist, now can it?

\\sarcasm

 

[Geezer]

In my example with precession you see that conservation of angular momentum does not hold true because there is not a net torque of zero.

Wrong again. There ARE other net (non-zero) torques acting on Earth, including due to the gravitational pull from other planets and the Sun.

 

[Geezer]

In fact the momentum goes to zero and then reverses direction which means the angular momentum associated with the precession effect is coming into and out of existence each time. This can not happen if conversation of angular momentum was true. Earth is not a closed system, the torques which are present over millions of years may have an effect on orbitals. The way most astrophysicists are applying conservation of momentum says this can not happen.

Angular momentum can vary in time with applied torques. There's nothing "unaccepted" about that. If the torques aren't constant (e.g., because the relative distance to other planets isn't constant...so that the torques due to the presence of other planets change with time), then angular momentum will change in time, too. It's just ordinary, Newtonian mechanics. To emphasize, this does NOT imply "conservation of angular momentum isn't true." You're wrong about that. It's been PROVEN that angular momentum is conserved for closed systems. The Earth, by itself, is NOT a closed system; Earth has a satellite, exists in a solar system with lots of other planetary bodies, and revolves around the Sun.

 

[Geezer]

That is exactly my point and the reason that conservation of momentum can not explain it by itself. To have conservation of angular momentum the net torque must be zero. For Earth, we know that it is not. The precession proves it. Orbits of planetary objects can not be reliably explained by conservation of angular momentum over millions of years.

I think you misunderstood some earlier posts. People said, "conservation of angular momentum" explains the precession, but what they meant--and how I interpreted it, even though it was explicitly stated as such--was that general principles of angular momentum and torque are the reason for the precession. Which. Is. Correct.

 

[AIR&SPACE]

I think you misunderstood some earlier posts. People said, "conservation of angular momentum" explains the precession, but what they meant--and how I interpreted it, even though it was explicitly stated as such--was that general principles of angular momentum and torque are the reason for the precession. Which. Is. Correct.

^ This

 

[Geezer]

Agree, that's the whole point, that Earth is not a closed system. Newton himself refused to remove the time element from his equations.

Why would he remove the time derivatives? The equations wouldn't be correct without them.

 

[IbrahimMisbah]

Well, thanks for all the replies.I understood the answer to the second question.If i am correct that implies that the substance that made up Earth was rotating themselves,right?
And do the two body system fall under the course of introductory mechanics course.I didn't find it anywhere!