- There are two types of reference frames: inertial and non-inertial frames. Inertial frames obey Newton's laws of motion while non-inertial frames do not. - The Earth is considered an inertial frame even though it rotates and revolves because the accelerations produced are small enough to be negligible. - In non-inertial frames, pseudo or fictitious forces appear even when no real forces are acting on an object. These forces arise due to the acceleration of the non-inertial reference frame.

1. • THEORY OF RELATIVITY
• INERTIAL AND NON INERTIAL FRAME OF
REFERENCE

2. Learning objectives
• Differentiate between inertial and non inertial
frames.
• Why the Earth is considered as inertial frame
of reference.
• Explains about Pseudo force.
•

3. WHAT IS FRAME OF REFERENCE?
• A frame of reference is a coordinate system
relative to which the position and motion of a
object may be described.
• To find the position of an object can we use
frame of reference.

4. Example 1
• Consider a bus is moving with a uniform
velocity say 30 kmph along a straight line on
the road. An observer A is sitting inside the
bus and another observer is standing on the
road(at rest ). Imagine a dog is running inside
the bus with speed 5kmph.
• For the observer A, dog velocity is 5 kmph
only .
• But for observer B, dog velocity is appears to
be 35 kmph.

5. Example 2
• Consider a moving train along a straight line. If
a person throws a ball upwards, its trajectory
will be straight vertical line. But for an
observer on the platform the ball takes
parabolic path.
• Both rest frame and moving frame are relative
to each other.

6. Space time coordinate
• In moving frame, time has to be measured on
a definite scale and is required to know the
position of moving particle. Then we must
assign one more coordinate. i,e time t. such a
reference frame is called space time
coordinate. It has 4 components.(x,y,z,t)

7. Types of frame of reference
• 1. Inertial frame of reference
• 2. Non inertial frame of reference

8. Inertial frame of reference
• A frame of reference which obeys Newton
laws of motion is called Inertial frame of
reference.
• Also called Galilean, Newtonian frame of
reference.

9. Inertial frame of reference
• In Newton second law, F= ma
• If force applied on the body F= 0, then
acceleration produced by the body is zero a=0.
but mass is not equal to zero.
• This inertial frame is also known as non
accelerating frame.
• Inertial frame is also called Non rotating frame
in case of rotational motion.

10. Earth is an inertial frame?
• Earth is revolving around the sun and
continuously in motion with change in its
velocity. Earth has both rotation and revolution
speed. But its speed is very less. The centripetal
acceleration w2R = 3.4 cm/s2 which is negligible
• If we toss a coin it comes back in vertical
direction. It will not take parabolic path. So earth
is an inertial frame.
• Otherwise it is difficult to calculate any values.

11. Non inertial frame of reference
• A frame of reference which doesn't obeys
Newton laws of motion is called non inertial
frame of reference.
• Non inertia means the frame of reference
which doesn't moves with uniform velocity.
• Here acceleration of the body is not equal to
zero.

12. Non inertial frame of reference
• Force applied on the body is zero but
acceleration is not zero.
• Hence this frame is also called accelerating
frame.

13. Examples
• 1. Any vehicle taking a turn.
• 2. Merry go round.
• 3. Sudden start or stop a vehicle.
• 4. Moving in a lift.

14. • If the force F=ma be acting on a particle in an
inertial frame S, the force acting in reference
frame S’. Then F’ = ma – ma0
• Here Newton’s second law is not valid. Put
F0=-ma0, F=ma
• - F’ = F + F0, if F=0, F’ = F0 = - ma0

15. Psuedo force
• A force which doesn't acts on the particle and
force actually doesn't exist. But appears to
come in the consequence of acceleration of
frame S’ with respect to frame S. This force is
called Pseudo force or fictitious force.

16. Coriolis force
• In case of rotational frame of reference
pseudo force is known as coriolis force.
• This is the observed acceleration in rotating
frame.
• An apparent force that arises because of the
earth spin around its axis. Freely moving
objects are deflected to right to their direction
of motion in the northern hemisphere and to
the left of their direction of motion in
southern hemisphere.

17. Examples
• Tidal winds
• Cyclones
• A fly walking on rotating fan.