Frames of Reference :
To define motion the observer must define a frame of reference relative to which motion is considered. A body in motion can be located with reference to some coordinate system called the frame of reference. The body is said to be at rest if the co ordinates of all the points of a body remains unchanged with time and with respect to the frame of reference. If the coordinates of any point of the body change with time, the body is said to be in motion.
Consider a body p at a the point A. Let x,y,z be the co ordinates with respect to the frame of reference. If body is at A all the time then it is said to be at rest. If another body Q is at A first and then at B (x,y,z) it is in motion with respect to the frame of reference. The observer O coincides the motion of p with respect to x,y,z. The observer O' coincides with respect to x', y',z'. If O and O' are at rest with respect to each other they will observe the same motion.
Examples :
1) Consider two observers A and B, A is on the earth, B is on the sun. Both observe the motion of the moon. To the person on the earth, moon will appear to move along a circular path. To the observer B, moon will appear in a wavy path. But to the observer on the ground the path of the point on the rim appears to be cycloid
2) Consider a person in a train moving with uniform velocity. If a stone is dropped by a person, to the person who drops it appears that the stone is falling down. To the person standing on the platform the stone is moving along a parabola.
3) Consider a person sitting in a train. All the windows of the train are closed. If a stone is thrown upwards then the stone comes back to the same position. This in the case of non-inertial frame of reference.
Inertial Frame of Reference :
In this frame of reference, newton's 1st and 2nd law holds good. In this no acceleration is observed for a particle, free of any force or any constraint. It is convenient to take a fixed star as a standard inertial frame of reference. For standard earth can be taken as inertial frame of reference. It's rotation about its own axis can be taken to be negligibly small.
Galilean Transformation :
Consider a particle P in a frame of reference. Let x,y,z be the co ordinates. The co ordinates are different if the inertial frame of reference chosen is different. Some times it is necessary to change co ordinates from one frame of reference to another frame of reference. This is called Galilean Transformation. Such a set of equations are called transformation equations.
Consider two inertial frames of reference S(x,y,z) and S' (x', y',z'). The observer O is in the reference frame S'. The observer moves with uniform velocity V relative to O along the x-axis. At time t=0, O and O' are coincident. After time t1,
OO'= Vt
Transformation of position :
Consider a particle p
Here r' =r + Vt
r = r' - Vt
V is parallel to x-axis, separating the vector equation into three components.
x' = x- Vt
y' =y
z' =z
t' =t ............(i)
It is observed that the two observers are using the same time. It means that the time, measurements are independent of motion of the observer...............Read
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To define motion the observer must define a frame of reference relative to which motion is considered. A body in motion can be located with reference to some coordinate system called the frame of reference. The body is said to be at rest if the co ordinates of all the points of a body remains unchanged with time and with respect to the frame of reference. If the coordinates of any point of the body change with time, the body is said to be in motion.
Consider a body p at a the point A. Let x,y,z be the co ordinates with respect to the frame of reference. If body is at A all the time then it is said to be at rest. If another body Q is at A first and then at B (x,y,z) it is in motion with respect to the frame of reference. The observer O coincides the motion of p with respect to x,y,z. The observer O' coincides with respect to x', y',z'. If O and O' are at rest with respect to each other they will observe the same motion.
Examples :
1) Consider two observers A and B, A is on the earth, B is on the sun. Both observe the motion of the moon. To the person on the earth, moon will appear to move along a circular path. To the observer B, moon will appear in a wavy path. But to the observer on the ground the path of the point on the rim appears to be cycloid
2) Consider a person in a train moving with uniform velocity. If a stone is dropped by a person, to the person who drops it appears that the stone is falling down. To the person standing on the platform the stone is moving along a parabola.
3) Consider a person sitting in a train. All the windows of the train are closed. If a stone is thrown upwards then the stone comes back to the same position. This in the case of non-inertial frame of reference.
Inertial Frame of Reference :
In this frame of reference, newton's 1st and 2nd law holds good. In this no acceleration is observed for a particle, free of any force or any constraint. It is convenient to take a fixed star as a standard inertial frame of reference. For standard earth can be taken as inertial frame of reference. It's rotation about its own axis can be taken to be negligibly small.
Galilean Transformation :
Consider a particle P in a frame of reference. Let x,y,z be the co ordinates. The co ordinates are different if the inertial frame of reference chosen is different. Some times it is necessary to change co ordinates from one frame of reference to another frame of reference. This is called Galilean Transformation. Such a set of equations are called transformation equations.
Consider two inertial frames of reference S(x,y,z) and S' (x', y',z'). The observer O is in the reference frame S'. The observer moves with uniform velocity V relative to O along the x-axis. At time t=0, O and O' are coincident. After time t1,
OO'= Vt
Transformation of position :
Consider a particle p
Here r' =r + Vt
r = r' - Vt
V is parallel to x-axis, separating the vector equation into three components.
x' = x- Vt
y' =y
z' =z
t' =t ............(i)
It is observed that the two observers are using the same time. It means that the time, measurements are independent of motion of the observer...............Read
Frames of Reference CLICK HERE
CLICK HERE to join this website for free
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