Chapter Kinematics

KINEMATICS

The branch of physics which deals with the study of the objects at rest and in motion is called mechanics.

It is further divided into two parts are:

1.Statics

Statics is the branch of mechanics which deals with the study of objects at rest.
An object can be at rest only when all the forces acting on it at equilibrium.Thus,we can say that it is the branch of mechanics which deals with the study of motion of objects under the effect of forces in equilibrium.Here, time factor does not play any role.

2.Dynamics

Dynamics is the branch of mechanics which deals with the study of objects at motion.

Dynamics further divided into two parts:

(i)Kinematics

Kinematics is the branch of mechanics which deals with the study of objects at motion without taking into account the factors (.i.e. nature of forces, nature of body etc)which cause motion.

(ii)Dynamics proper

Dynamics proper is the branch of mechanics which deals with the study of objects at motion taking into account the factors (.i.e. nature of forces, nature of body etc)which cause motion.

OBJECTS IN MOTION

Rest: An object is said to be at only if it does not change its position with time, with respect to its surroundings.

Motion: An object is said to be at only if it is changing its position with time, with respect to its surroundings.

REST AND MOTION ARE RELATIVE TERMS

It means an object in one situation can be at rest but in another situation the same object can be in motion.
i.e. A person sitting inside the moving train is at rest with respect to its fellow passengers but in motion with respect to the objects outside the train.
A person sitting inside the house is in rest with respect to earth but in motion with respect to other planets.

CONCEPT OF POINT MASS OBJECT OR PARTICLE

When an object in motion covers a very large distance as compare to the size of body or dimensions, then to study the motion of that object, its size or dimension is neglected and object is regarded as point object.
.i.e. 1.While studying the revolution of earth around the sun, the diameter of earth is very small as compared to the length of its orbit around the sun, the earth can be regarded as the point object.
2.A bike travelling a few thousand kilometer distance,can be taken as a point object.But, if bike is travelling a distance which is not very large as compared to its size then the bike can not be considered as a point mass object or particle.

TYPES OF MOTION OF A BODY

(i)Rectilinear motion or translatory motion:

Rectilinear motion: is that motion in which a particle or a point mass object is moving along a straight path(line).

Translatory motion: is that motion in which a body, which is not a point mass object is moving such that all its constituent particles move simultaneously along parallel straight line and shift through equal distance in a given interval of time.
.i.e. A body slipping along the inclined plane has translatory motion.

[Note:Rectilinear or translatory motion can be uniforn or non-uniform]

(ii)Circular or Rotatory motion

Circular motion: is that motion in which a particle or a point mass object is moving on a circle.

Rotatory motion: is that motion in which a object, which is not a point mass object, is moving such that all its constituent particles move simultaneously along concentric circles, whose centers lie on a line, called axis of rotation and shift trough equal angle in a given time.

Circular or rotatory motion can be two dimensional or three dimensional and can be uniform or non-uniform motion.If the circular or rotatory motion is uniform,it is periodic also.

(iii)Oscillatory motion or Vibratory motion

Oscillatory motion: is that motion in which a object(body) moves to and fro or back and forth repeatedly about a fixed point (called mean position) in a definite interval of time.
i.e. pendulum of wall clock is in oscillatory motion.etc
In oscillatory motion body have well defined limits (called extreme points) on either side of mean position.

Vibratory motion: If in the oscillatory motion,the amplitude is very small (microscopic) then motion is said to be vibratory motion.

In oscillatory or vibratory motion if the restoring force(torque) is in linear motion of the body is said to be simple harmonic motion.

FRAME OF REFERENCE

MOTION IN ONE,TWO AND THREE DIMENSION

(i)One dimensional motion:The motion is said to be one dimensional motion if only one out of three coordinates specifying the position of the object changes with respect to time.
OR
A motion is said to be one dimensional motion if only one out of the three coordinates changes with time.In this case object moves in a straight line and motion is called linear motion.

i.e.
A train running on a straight track.
An apple falling from the tree.

(ii)Two dimensional motion:The motion is said to be two dimensional motion if only two out of three coordinates specifying the position of the object changes with respect to time.
OR
A motion is said to be two dimensional motion if only two out of the three coordinates changes with time.In this case object moves in a plane.

i.e.
A caroom coin or a billiards ball in motion.
The earth revolving around the sun.

(iii)Three dimensional motion:The motion is said to be three dimensional motion if three out of three coordinates specifying the position of the object changes with respect to time.
OR
A motion is said to be three dimensional motion if three out of the three coordinates changes with time.In this case object moves in a space.

i.e.
1.Objects moving in the space.
2.A kite flying on a windy day.
3.Random motion of gas molecules.

MOTION IN STRAIGHT LINE

Scalar quantities or Scalars:Those physical quantities which have only magnitude(value) but no direction.
i.e. Mass,Length,Time,Distance covered,speed,Temperature,work etc.
(i)Generally scalars are numbers or digits.Where numbers show its magnitude.
(ii)Scalars can be added,subtracted,multiplied,and divided by ordinary laws of algebra.
(iii)Scalars is shown by modulus or by single letter.
(iv)Scalars can be positive or negative.
Vector quantities or Vectors:Those physical quantities which have magnitude as well as direction are called vector quantities or vector.
i.e. Displacement,velocity,acceleration,force,torque,gravitational intensity etc.
(i)Vectors can be represented by either a single letter in bold face or by a single letter with an arrow head on it.
(ii)Vectors can not be added,subtracted,multiplied,and divided by ordinary laws of algebra.Here we use law of vectors.

Path length or Distance and Displacement

Path length: is the actual distance(path or length) travelled by the object in a given time during motion.
(i)Distance is a scalar quantity as it have only magnitude.
(ii)Distance can not be negative or zero.(always positive)
(iii)Distance depends on path followed, as a result different path gives different values.
(iv)Distance never be less than displacement, can be equal or greater than displacement.

Displacement: is the shortest distance(path or length) between the initial and the final position of the object in a given time.And its direction is from initial to final position.
(i)Displacement is a vector quantity as it possesses both magnitude as well as direction.
(ii)Displacement can be negative or zero or positive.
(iii)Displacement do not depend on path followed(gives unique value), only depends upon the initial and the final position.
(iv)Displacement can be equal to distance or less than distance.

SPEED

Speed: of an object is defined as the ratio of total distance travelled upon total time taken.

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