I don't understand reference frames

[PhizKid]

I've read all sorts of descriptions in textbooks and online, but I don't get the purpose of reference frames. Why can't you just put everything on the same set of coordinate planes? I don't see what difference it makes. There was an example with a car traveling alongside another car, and that to each other, their velocities are 0. I don't get why this is because in reality they are just both traveling at the same speed. Is frame of reference just what something appears to an observer? When we solve physics problems, aren't we just observing as an omnipresent observer so that we see everything all at once?

Here is a sample question:

Car A is traveling towards the origin 800m away of an xy-plane on the positive x-axis at 80km/hr. Car B is traveling towards the origin 600m away on the same coordinate plane, but on the positive y-axis at 60km/hr.

a) Velocity of B with respect to A
b) Angle between this velocity and the line of sight between the two cars
c) If both cars maintain their velocities, do the solutions to parts a) and b) change as they move towards the origin?

For part a), I would naturally say 60 km/hr, but it says with respect to A. So that does mean, if I am inside car A, what velocity does it look like B is traveling at to me? I know there is some equation to solve this (something like V_pA = V_pB + V_BA), but I don't understand why the equation is true or how it works. We need two frames of reference and a moving particle, but I don't know what those are in this case. Since I am the observer inside car A, I would say the p is car B, but I don't know what the reference frames B and A are. I know one reference frames is probably myself inside the car I am in? I'm not sure.

Part b) I would say 90 degrees because the vehicles are perpendicular, but I'm not sure what angle car B would look like it's at to me if I was inside car A. I guess it would look a little to my right as I'm turning my head slightly right to see the car traveling closer to me.

Part c) I guess it would change because as car B nears me, it becomes closer to my front instead of on my right side and eventually when we both reach the origin, car B will be directly in front of me or something.

 

[PhizKid]

Also what I don't understand leads to inertial frame:

For example, we can assume that the ground is an inertial frame provided we can
neglect Earth’s astronomical motions (such as its rotation).

Why do we have to neglect rotation?

That assumption works well if, say, a puck is sent sliding along a shortstrip of
frictionless ice — we would find that the puck’s motion obeys Newton’s laws.
However, suppose the puck is sent sliding along a long ice strip extending from
the north pole. If we view the puck from a stationary frame in space,
the puck moves south along a simple straight line because Earth’s rotation
around the north pole merely slides the ice beneath the puck. However, if we
view the puck from a point on the ground so that we rotate with Earth, the puck’s
path is not a simple straight line. Because the eastward speed of the ground be-neath the puck is greater the farther south the puck slides, from our ground-based view the puck appears to be deflected westward. However, this
apparent deflection is caused not by a force as required by Newton’s laws but by
the fact that we see the puck from a rotating frame. In this situation, the ground is
a noninertial frame.

Ok, if we view this puck from space, I can see how it would travel down a straight line, I guess. But if we view it from the ground, I can see it still traveling down a straight path. How is the puck traveling in a deflective motion? If you shoot a hockey puck straight towards a goal, it looks like it is traveling straight. If the puck continues its motion in the straight line, won't it continue to look straight until it finally disappears from our line of sight?

 

[gneill]

Also what I don't understand leads to inertial frame:

An inertial frame is one in which bodies without external forces move according to Newton's first law. For this to be true the frame of reference should have no intrinsic accelerations associated with it.

Why do we have to neglect rotation?

We don't HAVE to neglect rotation, but if we choose a frame that accelerates then the frame is no long inertial and the math gets hairy
Sometimes a rotating reference frame is ideal for certain problems, particularly if there is some rotational symmetry that can be taken advantage of.

Ok, if we view this puck from space, I can see how it would travel down a straight line, I guess. But if we view it from the ground, I can see it still traveling down a straight path.

No, it only appears to be a straight path over short distances and short times. This is an approximation we make when we assume that a frame of reference associated with the Earth's surface is an inertial frame. It simplifies our mathematics, and it really is a pretty good approximation for "local" physics given the slow rotation rate and relatively gradual curvature of the Earth's surface.

How is the puck traveling in a deflective motion? If you shoot a hockey puck straight towards a goal, it looks like it is traveling straight. If the puck continues its motion in the straight line, won't it continue to look straight until it finally disappears from our line of sight?

In science and pure mathematics there is a vast difference between "looks" and "is"

Choosing a suitable reference frame or assuming appropriate approximations can simplify the mathematics of a problem; You don't have to be adding or subtracting 'reference' motions from all your variables and constants.

If you choose a frame that is not-inertial, that is, it has some intrinsic acceleration (which includes centripetal acceleration due to rotation), then the math demands that you introduce what are called 'fictitious' forces to account for the observed deviations from inertial motion for objects that have no other forces acting.

Think of Newton's first law; A body in motion will continue in a straight line at constant speed unless acted on by an external force. Such an object observed from an accelerated frame of reference will not appear to move in a straight trajectory, even though no source for external force acting on it is observed.

 

[PhizKid]

No, it only appears to be a straight path over short distances and short times. This is an approximation we make when we assume that a frame of reference associated with the Earth's surface is an inertial frame. It simplifies our mathematics, and it really is a pretty good approximation for "local" physics given the slow rotation rate and relatively gradual curvature of the Earth's surface.

Okay, but then from space, wouldn't the puck also look like it's moving in a curve?

We haven't learned Newton's laws yet, but it's the very next chapter and I'm reading ahead. This is similar to what we learn as children 'an object in motion stays in motion' or something similar, right?

So an inertial frame on Earth would be if Earth had no friction on its surface at all, and no air?

So if a puck keeps moving from the north pole to the south pole in a straight line, how is it curving from the view on the surface of the Earth if the Earth is not rotating? If the movement from space is viewed as a straight line, then I don't understand how a view from Earth wouldn't be just a straight line down.

 

[gneill]

Okay, but then from space, wouldn't the puck also look like it's moving in a curve?

Sure, the observer has to take into account all the forces acting including gravity.

A better scenario might be that of a puck moving in empty space. To an observer in an inertial frame watching the puck it would move in a straight line at constant speed. Observed from a rotating frame, it would appear to move in a curve.

We haven't learned Newton's laws yet, but it's the very next chapter and I'm reading ahead. This is similar to what we learn as children 'an object in motion stays in motion' or something similar, right?

Yes, something similar.

So an inertial frame on Earth would be if Earth had no friction on its surface at all, and no air?

The frame of reference doesn't specify nor depend upon what physical forces do or don't act. It just specifies the reference to which the physics equations refer. It's like setting up your coordinate axes and choosing the origin.

In truth, there are NO inertial frames attached to the Earth because of its rotation and motions through the heavens. However, that does not prevent us from making suitable approximations when allowed. A frame of reference attached to the surface is very, very nearly inertial for physics done "locally" (relatively small distances and times).

So if a puck keeps moving from the north pole to the south pole in a straight line, how is it curving from the view on the surface of the Earth if the Earth is not rotating? If the movement from space is viewed as a straight line, then I don't understand how a view from Earth wouldn't be just a straight line down.

The Earth's surface is curved. The actual trajectory in space is a 3d curve. If the view from space is "from the side", then the curve will form a half circle.

 

[PhizKid]

Ok, so then reference frames are basically just separate coordinate axes. What does it mean when an object is on a set of coordinate axes from another object in a different set of coordinate axes? Doesn't that mean it's in another space or dimension or something and it's impossible to calculate the relativity between the two objects? If both objects were in some position on Earth, wouldn't they both be on the same set of coordinate axes, no matter where they are? I don't see how it makes sense to make another set of axes just because you're viewing the object from a different point of view.

 

[gneill]

Reference frames are just points of view. The same objects exist in an infinite number of reference frames; the objects are the same objects, just the "point of view" is different. There's a whole subject devoted to transforming coordinates from one frame to another. This becomes particularly important in Relativity.

There's nothing absolute about any particular frame of reference. There is no Exalted High Universal Frame that supersedes all others. Saying that something is at such and such a point moving at a certain speed in some frame of reference does not mean that it's the only frame of reference that the object exists. It's just that some frames of reference are more convenient for some purposes than others. Not all reference frames are equally useful for all situations.

Suppose someone insisted that you use the a reference frame anchored to the center of Sun to measure the floor in your house for new carpet. After all, the center of the Sun is much a more "inertial" and stable frame of reference for our solar system than is any point on the Earth which whirls about the Sun and rotates at the same time. How easy would it be to determine the coordinates of the corners of your room in such a case? How would the installer find your house?

 

[PhizKid]

So the reference frame of the center of the sun is like saying, if the sun was viewing something, like my house?

 

[gneill]

So the reference frame of the center of the sun is like saying, if the sun was viewing something, like my house?

Yes. Imagine an observer there who has erected a set of coordinates and is measuring everything from there and expressing it in those coordinates.