Thursday, August 2, 2012

Physics-Inertial Frame

The idea of an inertial frame is that there are no external forces acting upon the frame. All inertial frames are not accelerating with respect to another inertial frame. Thus you can apply a galilean transformation to the frame, which basically means that you can calculate motion in one frame in the same way you calculate motion in another frame.

As an example let us consider a baseball in parabolic motion. It has a v0 = 40 m/s with an angle 30 degrees above the horizontal. It has a vertical v0 = 20 m/s and a horizontal v0 = 20(3)1/2. It reaches its peak around 2 seconds in flight and will return to the initial height at around 4 seconds, with its vertical velocity oriented in the other direction. It will then get to travel around 80(3)1/2 meters in this time frame.

Although there is a force acting on the baseball, it is within the system we already considered. Thus if we transform to another reference frame, we can repeat this calculation and get a new trajectory in this new frame. Let us take a reference frame that is moving 20 m/s in the same direction of the horizontal path of the baseball. We would then calculate the same v0 in the vertical direction, which gives us the same flight time, however the horizontal position in this frame would only be 4[20(3)1/2-20] which would be around 56 m. as opposed to the 136 m in the other frame. However once you transform this back to the original reference frame, you would get the same path of motion for the baseball.

Its also entirely possible to calculate in the reference where the ball moves only up and down, and has no horizontal motion. This would be the reference frame that has a velocity of 20(3)1/2 in the direction of motion of the baseball. If there are no forces acting on an object you can always transform to a frame in which it is stationary. However in the case of this baseball, theres the addition of the force of gravity pulling it down for parabolic motion. Thus we can't transform to its completely stationary frame without adding in a force to the frame itself, making it an accelerating frame. Viewing objects in this frame would create imaginary forces on certain objects causing a lack of parity between frames.

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