GR: Inertial Systems & Direction Changes of Motion

In summary, when a canon shoots a ball straight up (one dimension), the ball only accelerates as long as the nongravitational force of the canon acts on it. After that, the ball decelerates in the gravity field until the point it turns back and accelerates in the opposite direction as it falls back on earth.
  • #1
Ratzinger
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When a canon shoots a ball straight up (one dimension), the ball only accelerates as long as the nongravitational force of the canon acts on it. After that, the ball decelerates in the gravity field until the point it turns back and accelerates in the opposite direction as it falls back on earth.

So is it right to say that according to GR, not only the freely falling body, but also the upmoving and 'turning point' frame are inertial, since no non-gravitational force acts on them?

But doesn't the ball notice the direction change of its motion? Is that because there are (at least) three local inertial systems?
 
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  • #2
I'm pretty sure you're confusing special relativity's inertial frames with GR's inertial frames. In GR, in an inertial frame, particles don't go in straight lines, they go in geodesics. In this case, the ball's trajectory is a geodesic.
 
  • #3
Ratzinger said:
When a canon shoots a ball straight up (one dimension), the ball only accelerates as long as the nongravitational force of the canon acts on it. After that, the ball decelerates in the gravity field until the point it turns back and accelerates in the opposite direction as it falls back on earth.
So is it right to say that according to GR, not only the freely falling body, but also the upmoving and 'turning point' frame are inertial, since no non-gravitational force acts on them?
But doesn't the ball notice the direction change of its motion? Is that because there are (at least) three local inertial systems?
In the ideal case of no air resistance: in GR there is only one locally inertial frame of reference in this case: that of the cannon ball.

The cannon ball's acceleration w.r.t. the supported cannon's non-inertial frame of reference is always negative - 'downwards', whereas, initially, the cannon ball's velocity is 'upwards'.

That 'upwards' velocity is first reduced to zero by the negative acceleration before becoming a 'downwards' velocity and then eventually it would fall straight back down the cannon's mouth. [Well you did say: "a canon shoots a ball straight up (one dimension)"!]

In the cannon ball's frame of reference it is in free fall and feels no acceleration.

Therefore the cannon would not notice the change of direction unless it had an altimeter on board, when the reading would reach a maximum, the cannon ball is in free fall all the time. It is the ground and the cannon that are not in an inertial frame of reference, that is why the cannon weighs so much!

I hope this helps.

Garth
 
Last edited:
  • #4
I hope this helps.
It did. No it looks easy. Thanks, Garth.
 

1. What are inertial systems in relation to motion?

Inertial systems are frames of reference in which Newton's laws of motion hold true. This means that an object at rest will remain at rest, and an object in motion will continue to move at a constant velocity, unless acted upon by an external force. Inertial systems are important in understanding the principles of motion and are commonly used in physics.

2. How do inertial systems relate to GR (General Relativity)?

In General Relativity, inertial systems are used to describe the motion of objects in a curved space-time. This means that the laws of motion in an inertial system may differ from those in a non-inertial system, such as one experiencing acceleration or gravity. Einstein's theory of General Relativity provides a more comprehensive understanding of motion in relation to inertial systems.

3. What is the difference between an inertial and non-inertial system?

An inertial system is one in which an object will continue to move at a constant velocity unless acted upon by an external force. In contrast, a non-inertial system experiences acceleration or is subject to external forces, causing the object to deviate from a uniform motion. Examples of non-inertial systems include an object in free fall, or one experiencing circular motion.

4. How do direction changes of motion affect inertial systems?

In inertial systems, direction changes of motion are caused by external forces acting on an object, such as friction or gravity. These forces can cause an object to accelerate or change direction, altering its velocity and thus affecting the motion of the object. In General Relativity, these direction changes are explained by the curvature of space-time and the influence of gravity.

5. Can inertial systems be used to predict the motion of objects?

Yes, inertial systems can be used to predict the motion of objects, as they follow the principles of Newton's laws of motion. However, in non-inertial systems, such as those affected by gravity or acceleration, the motion may be more complex and require additional factors to be considered. In these cases, the principles of General Relativity can be used to accurately predict the motion of objects in space and time.

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