Space and Time, Physics tutorial

Introduction:

Everything in universe is in steady motion comprising tree or the rock which you possibly believe is not moving. This covers topics which comprises frame of reference, space and time will assist you to know that all motion is relative. This signifies that objects in universe move relative to one another.

Frame of Reference:

In the frame of reference, rest and motion, relative motion, inertial and non-inertial frame of reference and related issues are discussed.

Rest and motion:

To understand the concept of frame of reference it is essential to know certain observations which have been made by physicists about physical world we are living in. One of such observations is that body is said to be at rest when it doesn't change its position with time. It is said to be in motion when it changes its position with time. But if position of the object changes with time or not, we need the point completely fixed in space to be known. Such a fixed or stationary point is not known to exist in universe. Due to this physicists have observed that everything in universe is in constant motion comprising the earth we are living in. Earth revolves round sun and at the same time rotates round polar axis.

Planets are also in motion with respect to each other. If the wrist watch you place on surface of the earth appears to be at rest it is really in motion as earth in which it rests is in motion. We can say that wrist watch is in motion relative to earth. This signifies that there is nothing like complete rest position for any object. When we say that wrist watch you put on ground is at rest we indicate that it doesn't change position with respect to earth. Rest here signifies relative rest. It is always significant for you to keep in mind that the body is at relative rest with respect to another when it doesn't change its position relative to latter. To understand this concept of relative rest better, think of passengers sitting in the luxury bus moving along the road. Passenger is at relative rest with respect to other passengers in same luxury bus whereas he or she is really moving with respect to objects along the road side.

Specifying Frame of Reference:

Every object is at rest or in motion relative to another object; it denotes that position or motion of object can be chosen with reference to the fixed point in the rigid frame work. This so called fixed point is known as ORIGIN, O. At this point, this is the origin draw three mutually perpendicular axes to signify X, Y and Z axes respectively. So initial position of the object or final position of the object can be designed with reference to the fixed frame work X, Y and Z axes at origin. This applies to all kinds of objects be it a particle, or system of particles or the rigid body. We thus describe FRAME of REFERENCE as rigid or fixed frame work, relative to which position and movements of the particle or of a system of particles, or of a rigid body may be estimated. If coordinates of object remain fixed in spite of the elapse of time, we can say that object is at rest. But if the change takes place in one, or two, or all three coordinates with time, then object is said to be in motion.

Inertial and Non-inertial Frame of Reference:

Inertial frame of reference is the frame of reference which explains time and space evenly, isotropically, and in the time-independent manner.

All inertial frames are in the state of constant, rectilinear motion regarding one another; the accelerometer moving with any of them would notice zero acceleration. Measurements in one inertial frame can be converted to measurements in another by the simple transformation. In general relativity, in any region small enough for curvature of spacetime to be insignificant, one can find the set of inertial frames which roughly explain that region.

The coordinate system in which motion of any object relies only on interactions of constituent particles among themselves is known as the inertial frame of reference. In such frames, Newton's laws of motion holds good.

The non-inertial reference frame is the frame of reference which is going through acceleration regarding an inertial frame. The accelerometer at rest in the non-inertial frame will in general notice the non-zero acceleration. In the curved spacetime all frames are non-inertial. Laws of motion in non-inertial frames do not take simple form they do in inertial frames, and laws differ from frame to frame depending on acceleration. In a non-inertial frame, the motion of the objects is partly due to interactions among constituents' particles and partly due to the movement of the frame with respect to an inertial frame.

Concept of space:

Cartesian Coordinates:

There are different ways to specify the point in space. In one of the ways to state the point in space, we need to know the coordinates along two or three mutually intersecting straight lines fixed at some rigid point known as the origin. These intersecting straight lines are known as axes of reference. Distances from point in space to axes are found by drawing parallel lines from it to axes. When axes of reference are mutually perpendicular to each other for instance, in the two dimensional plane, they are known as rectangular axes. When they are inclined to each other at the angle, other than the right angle, they are known as oblique axes. Coordinates referred to either rectangular or oblique axes are known as Cartesian co-ordinates.

Polar Coordinates:

Polar coordinates give the method of rendering graphs and signifying positions of points on the two-dimensional (2D) surface. Polar coordinate system is used in physics, mathematics, navigation, robotics, engineering and other sciences.

Polar plane comprises of the reference axis, or ray, which originates from the point known as origin. Positions or coordinates are found according to distance or radius, from origin, symbolized r, and angle relative to reference axis. In the most common polar system, reference ray points off toward the right, and angles are estimated counterclockwise from it.

Points or coordinates in either system are specified by writing the opening parenthesis, the r value, a comma, the θ value, and the closing parenthesis in that order. Radius coordinates are, by convention, always nonnegative. Angles can be indicated in degree s from 0 to 360, or in radian s from 0 to 2 pi, where pi is about 3.14159. The example using degrees is (r, θ) = (2, 30). The origin is assigned r = 0.

If the scheme in the left-hand illustration is used, it is possible to convert a coordinate in the Cartesian xy -plane to polar values using these formulas:

x = r cos θ

y = r sin θ

Conversely, to convert a coordinate in the polar plane to Cartesian values, use these formulas:

r = (x2 + y2)1/2

θ = arctan (y / x)

Concept of Time:

The complete day comprises of day time and night time segments of earth's rotation. As during day time segment we see sunlight but in the night time segment sunlight is hidden from us and we see only darkness. The sun becomes visible to us to move across sky due to this diurnal rotation of the earth about the polar axis. The meridian at the place is an imaginary vertical plane through it. Sun is said to be in meridian when it reaches the highest position in the course of the evident journey in the sky. The interval of time between two successive transitions of centre of the sun's disc across the meridian at any place is known as a solar day. Length of this solar day differs from day to day due to several reasons but same cycle of variations repeats after the solar year that is 365½ days, approximately. Mean of actual solar days averaged over the complete year is known as mean solar day. The clock, watch or chronometer keeps mean solar time. Time interval between successful appearances provides standard of time. This was the situation before 1960. With developments in science, standard of time was changed to periodic time of the radiation equivalent to transition between two energy levels of the fundamental state of atom caesium-133. Mean solar day is divided in 24 hours. An hour is divided in 60 minutes and a minute is divided in 60 seconds.

Thus, mean solar day = 24hrs x 60min x 60secs = 86,400 mean solar Seconds.

This signifies that mean solar second is 86,400th part of mean solar day. This provides unit of time called as second. By using standard of time as periodic time related with the transition between two energy levels of cesium-133 atom, 1 second = 9, 192,631,170 cesium periods.

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