# How can an object have an acceleration of 9.81m/s^2 when there is

1. Feb 14, 2013

### student34

no change in velocity? How can a rock that isn't moving have acceleration?

2. Feb 14, 2013

### JimJam

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Acceleration is the rate of change of velocity, isn't it? So it is speeding up in whatever direction 9.81m/s every second, therefore there must be a change in V?

3. Feb 14, 2013

### Staff: Mentor

Re: How can an object have an acceleration of 9.81m/s^2 when there is

It cannot have a (net) acceleration in a frame where it stays at rest.
It can have forces acting on it (like gravity, and a force from the floor), but they have to cancel.

4. Feb 14, 2013

### student34

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Hmmm, then there must be another definition of acceleration other than a change in velocity. Unless a change in velocy only applies to net acceleration.

5. Feb 14, 2013

### student34

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Sorry, I meant that it does not make sense to me that still object has acceleration g. There is no change in velocity, yet Einstein says that it has the same acceleration as something that has a changing velocity.

6. Feb 14, 2013

### JimJam

Re: How can an object have an acceleration of 9.81m/s^2 when there is

As in the object may be running parallel to an object with the same acceleration, in the same direction, so they have no relative movement between the two?

Last edited: Feb 14, 2013
7. Feb 14, 2013

### Drakkith

Staff Emeritus
Re: How can an object have an acceleration of 9.81m/s^2 when there is

First, are we talking about simple classical acceleration, or about General Relativity?
In classical physics the answer is that an object that isn't changing velocity has no acceleration. Gravity provides a force on an object, but for those on the ground there is no acceleration. The force on an object is equal to the force that would accelerate that object at 9.8 m/s2.

8. Feb 14, 2013

### student34

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Oh, I am in the first year of university physics, and we have not got to relateivity yet. They should probably have told us that a change in velocity is true except for with g. That really screwed me up.

9. Feb 14, 2013

### WannabeNewton

Re: How can an object have an acceleration of 9.81m/s^2 when there is

No it is always true that $\sum F_{i} = m\sum a_{i} = m\sum \frac{\mathrm{d} v_{i}}{\mathrm{d} t}$ for a single particle constant mass system (the indexes label the motion coupled to the respective force). The point is that when you place a pebble on the ground, there is an upwards reaction force from the ground on the pebble (loosely put it arises out of the electrostatic repulsions between the pebble and the ground) and this reaction force just happens to cancel out the weight of the pebble so that the net acceleration given above vanishes.

10. Feb 14, 2013

### student34

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Then why do they tell us that acceleration is a change in velocity all thoughout our textbook?

11. Feb 14, 2013

### WannabeNewton

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Because it is; What has been said thus far that has contradicted that?

12. Feb 14, 2013

### elfmotat

Re: How can an object have an acceleration of 9.81m/s^2 when there is

The rock has an "acceleration due to gravity" which is -9.8 m/s2. It has an "acceleration due to the ground" which is +9.8 m/s2. Add them together and you get zero.

13. Feb 14, 2013

### Staff: Mentor

Re: How can an object have an acceleration of 9.81m/s^2 when there is

There are two kinds of acceleration.

First, there is coordinate acceleration. This is the second time derivative of position, or the first time derivative of velocity. You don't get coordinate acceleration without change in velocity.

Second, there is proper acceleration. This is the acceleration measured by an accelerometer. Most likely you currently have a proper acceleration of 9.8 m/s² upwards although I suspect that you probably consider yourself to be at rest thus having a constant velocity of 0. So proper acceleration can be non-zero even with zero change in velocity.

14. Feb 14, 2013

### DrGreg

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Acceleration and velocity are always relative to something. You need to know what the "something" is, or is assumed to be, before you can say whether an object is accelerating or not.

In Newtonian physics we measure acceleration relative to the Earth's surface.

In General Relativity we measure (proper) acceleration relative to falling objects.

15. Feb 14, 2013

### student34

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Oh, so are you saying that to a rock falling, a different still-object will seem to be accelerating - hence relativity?

16. Feb 14, 2013

### student34

Re: How can an object have an acceleration of 9.81m/s^2 when there is

So a rock with zero velocity and zero speed has velocity!?

You may as well type Chineese instead of those formulas because it would mean the exact same to me.

17. Feb 14, 2013

### cepheid

Staff Emeritus
Re: How can an object have an acceleration of 9.81m/s^2 when there is

A rock sitting on the ground has zero acceleration because zero net force acts on it. Period. That's it. It doesn't have an acceleration of g.

18. Feb 14, 2013

### Whovian

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Well, it has zero velocity. I don't quite understand. (The formulas were saying that "the sum of the forces on an object is mass * acceleration, or the sum of the accelerations depending on if you define acceleration to be the total change in velocity or the result of the force, in which case the total acceleration, or the change in velocity, is just the sum of the accelerations." A little wonky.)

19. Feb 14, 2013

### DrGreg

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Yes. If a rock falls, there's 2 ways to look at it.
1. The rock is accelerating downwards relative to the ground.
2. The ground is accelerating upwards relative to the rock.
The revolutionary aspect of General Relativity was to base it on (2) instead of (1).

20. Feb 14, 2013

### student34

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Wow, thanks!

21. Feb 15, 2013

Re: How can an object have an acceleration of 9.81m/s^2 when there is

It's all about the reference frames.

22. Feb 15, 2013

### ehild

Re: How can an object have an acceleration of 9.81m/s^2 when there is

At the instant when you release a stone it has zero velocity, but a very short time Δt later the velocity is gΔt. Acceleration is defined as change of velocity over change of time: a =Δv/Δt. From zero to Δt the velocity changed by gΔt, divided by Δt it is g.

Newton's second law says that the acceleration is equal to the resultant force divided by the mass of the object.
The Earth pulls all objects with the force of gravity G=mg where g is about 9.8 m/s^2. If the object is released it accelerates downward: ma=G, a=G/m=g, with acceleration g. If the object is supported, sits on a table for example, the table exerts a force N (normal force) on it that prevents the object from falling: the object does not move, no change of velocity, the acceleration is zero, as the sum of the downward force of gravity and the upward normal force cancel: N-G=ma=0.

ehild

23. Feb 15, 2013

### A.T.

Re: How can an object have an acceleration of 9.81m/s^2 when there is

Here the 2 ways visualized:

24. Feb 15, 2013

### mikemeg

Re: How can an object have an acceleration of 9.81m/s^2 when there is

I could be wrong, but I think we're going wayyyyy beyond what the original poster was talking about. A lot of questions are not particularly deftly phrased in textbooks.

"g", commonly referred to as "the acceleration due to gravity" can be used for calculations without the object actually accelerating. You can think of it as "a falling object would accelerate at 9.81 m/s2," and that gives you a sense of the gravitational field. Dimensionally, m/s2 is the same as N/kg. So you could equally think of "g=9.81m/s2 near the earth's surface" as "there's a gravitational force of 9.81N for every kg of mass near the earth's surface".

In other words: "there's a 5kg rock. The acceleration due to gravity is 9.81" tells you that the weight of the object, mg, is 5kg*9.81m/s2 = 49.05 N.

25. Feb 15, 2013

### A.T.

Re: How can an object have an acceleration of 9.81m/s^2 when there is

I don't think so. In post #5 he clarified that he actually asks about Einstein's General Relativity where objects at rest on the Earth’s surface have a proper acceleration upwards of 1g.