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inertial frame of reference: in most of the cases , a frame of reference on the surface of the earth in the surroundings of the particle that we want to observe. OTHER frames of reference could be any object with constant velocity respect to the frame of reference on the surface of the earth.
Non inertial frame of reference: an elevator in free falling
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I perfect example of a frame of reference could be considered a lighthouse. Think of a grid with the point (0,0) being the light house. Now say we are sailing in towards the light house, if we are coming in towards the north, our point of reference would be the lighthouse, and on our own separate grid we are point (0,0) as well. The difference is however, we are exactly 2 kilometers (kliks, or 2,000 meters) north of the light house. We are traveling at a rate of 100 meters per second. ( 20 m/s). I would call up the light house and let them know we will be arriving in precisely 100 seconds. My point of reference would be the light house, while the origin would be where we originally started our journey from. The light houses point of reference would be where we originally set sail from, and the light houses origin would be the light house even though it hasn't moved.
If we were coming in from the East, and we made sure to tell our pals at the lighthouse to set the X axis towards the East, and the Y axis towards the North. We would let them know our velocity, speed, our origin (their point of reference), and our current location respectively. If our X axis was scaled to 1 kilometer per one X value. We would say "Our origin is directly 2 kilometers to the east of you." Our current location is (1,0) due to the fact that we are 1 mile away from our point of reference (lighthouse). When we arrive at the light house our coordinates will be (0,0).