Motion (Kinematics) Notes for SSC CGL, CHSL & Railways 2019

Motion (Kinematics) Notes for SSC CGL, CHSL & Railways 2019


Motion

When an object changes its position with respect to its surroundings with time.

Rest

When an object doesn’t change its position with respect to its surroundings with time.

NOTE:

  • Rest and position are relative terms, i.e., an object in one situation can be at rest but in other situation same object can be in motion.
  • No force is required for an object to be in uniform motion.

TYPES OF MOTION

1. Rectilinear Or Translatory Motion

When a particle or a body moves along a straight path, its motion is Rectilinear or translatory motion.

2. Circular and Rotatory Motion

  • Circular Motion: When a body moves in a circular path.
  • Rotatory Motion: When a body spins about its own axis.
  • Direction of motion changes at every point in Uniform Circular Motion. This direction is given by a tangent drawn at that point.

3. Oscillatory and Vibratory Motion

When a body moves to and from or back and forth repeatedly about a fixed point in a definite interval of time, it is said to be in oscillatory motion.

  • Amplitude: The extent to which the body moves on either side of a fixed point.
  • Vibratory Motion: The oscillatory motion, where the amplitude is very small.

One, Two and Three Dimensional Motion

1-D Motion (Motion in a line)

When position of an object changes only along one axis.

2-D Motion (Motion in a plane)

When position of an object changes along any two axis. ex: motion of a planet around the Sun.

3-D Motion (Motion in space)

When position of an object changes in all the 3 axes.


Basic Terms

Distance

Distance is the actual path traveled by a body in a given period of time.

  • Odometer – device used to measure distance traveled by the vehicle
  • Scalar quantity
  • SI unit: m

Displacement

Displacement is the shortest distance between any two points.

  • The change in the position of the object in a given period of time.
  • Vector quantity
  • SI Unit: m
   NOTE:
   Displacement may be positive, negative or zero whereas distance is always positive.
   |Velocity| ≤ Speed

Speed

Distance traveled by a moving object in unit time interval is called speed.

   speed = Distance / Time
  • Scalar quantity
  • SI unit: ms-1
  • Instantaneous speed: The speed of an object at any particular instant of time. limΔt→0(Δs/Δt) = ds/dt
  • Uniform Speed: If an object covers equal distance in equal intervals of time.
  • Non-uniform (Variable) Speed: If an object covers unequal distance in equal intervals of time.
  • Average Speed: Total Distance Covered / Total Time Taken

Velocity (AKA Speed with direction)

The velocity of a moving object is defined as the displacement of the object in unit time interval.

   velocity = displacement / time
  • Vector quantity
  • SI unit: ms-1
  • Uniform Velocity: If a body covers equal displacement in equal intervals of time.
  • Non-uniform (Variable) Velocity: If a body covers unequal displacement in equal intervals of time
  • Average Velocity: Vavg = (u + v) / 2
  • Relative Velocity
    = Va + Vb (if two bodies (a and b) travel in opposite direction)
    = Va – Vb (if two bodies (a and b) travel in same direction)

Acceleration (a)

Acceleration of an object is defined as the rate of change of velocity per unit time.

   a = (v-u) / t or a = Δv/Δt
  • SI Unit: ms-2
  • a is +ve, if it is in the direction of velocity and a is taken as -ve, if it is opposite to the direction of velocity.
  • Uniform Acceleration: If the object travels in a straight line & its velocity changes uniformly in equal intervals of time.
  • Non-uniform Acceleration: If the object travels in a straight line & its velocity changes non-uniformly in equal intervals of time.
  • Average Acceleration: Change in velocity divided by an elapsed time. aavg = (Vf – Vi) / (tf – ti)
  • Instantaneous Acceleration: acceleration at any particular instant of time.

NOTE: If u > v, a is deceleration or retardation

Equations of motion

v = u + at
s = ut + 1/2 at2
v2 = u2 + 2as

Circular Motion

Circular motion

Time Period

Time taken by an object to complete one revolution.

Frequency

No. of revolutions completed by the object on its circular path in a unit time.

Relation between Time Period and Frequency

   f = 1 / T

Angular Displacement (θ)

The angle subtended at the centre of a circle by a body moving along the circumference of the circle is called the Angular Displacement of the body.

  • SI Unit: radian (rad)
  • Angular Displacement = Arc / Radius

Angular Velocity (ω)

   Angular Velocity = Angular Displacement / time
   ω = θ / t

Angular Acceleration (α)

The angular acceleration of an object moving around a circular path is defined as the time rate of change of its angular velocity.

  • It occurs due to the change in direction of angular velocity. So its direction is also normal to the plane of circle in accordance with the direction change of angular velocity.
  • SI Unit: radian / (sec)2

Centripetal Force

When a body is in a circular motion, a force always acts on the body towards the centre of the circular path, this force is called centripetal force.

  • If a body of mass m is moving on a circular path of radius r with uniform speed v, then the required centripetal force:
  • F = mv2 / r

Relation between Linear and Angular Velocity

     v = r x ω

Relation between Linear and Angular Acceleration

     a = r x α

Centripetal Acceleration (ac)

Acceleration acting on a particle undergoing a uniform circular motion towards the centre of the circle is called centripetal acceleration.

     ac = v2 / r 

Centrifugal Force

An inertial force directed away from the axis of rotation that appears to act on all objects when viewed in a rotating frame of reference.

  • Pseudo Force
  • It is equal and opposite to centripetal force.

Application of centripetal and Centrifugal forces:

  • Roads are banked at turns to provide required centripetal force for taking a turn.
  • The cream is separated from milk when it is rotated in a vessel about the same axis.
  • The gravitational force of attraction between earth and sun acts as centripetal force.
  • Orbital motion of electrons around the nucleus.
  • Cyclist inclined itself from vertical to obtain required centripetal force.

Free Falling Objects

The objects falling towards the earth under the gravitational force alone, are called free falling objects and such fall is called as free fall.

  • g = 9.8 ms-1
  • Though the value of g is independent of free falling mass, a feather falls much slowly than a coin when released from a height. This is due to the resistance offered by air to the falling mass.
  • If released at the same time in vacuum, they would reach at the earth surface at the same time.
  • a +ve, if object falls vertically downward, a -ve, if object falls vertically upward
  • If object is thrown vertically upward, its final velocity is zero.
  • If object is thrown vertically downward, its initial velocity is zero.

Projectile Motion

When an object is thrown obliquely near the earth’s surface, its motion on a parabolic path is known as Projectile Motion.

  • The path followed by the object is called as Trajectory.

Projectile motion


Graphical Representation

1. Distance Time Graph

The change in the position of an object with time can be represented on the distance-time graph.

  • The distance time graph for a body moving at uniform speed is always a straight line as distance travelled by the body is directly proportional to time.
  • The distance time graph for a body moving with non-uniform speed is a curve.
  • The distance time graph is parallel to time axis when the object is at rest.
  • Slope of Distance Time graph gives average velocity.

distance time graphs

calculation-of-speed

2. Velocity Time Graph

The variation in velocity with time for an object moving in a straight line can be represented by a velocity-time graph.

  • Slope of velocity time graph of moving body gives its acceleration.
  • Area of v-t graph gives distance

velocity time graph


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