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Newton's Laws Of Motion & Friction

4. Reference Frames

4. Reference Frames
Whenever the observer is situated in space that is called the frame of reference. The reference frame is associated with a co-ordinate system and a clock to measure the position and of the events happening in space.
Types of Reference Frames :
4.1 Inertial Reference Frame
4.2 Non-inertial Frame
4.1 Inertial Reference Frame:
(a) A reference frame in which Newton’s first law is valid is called an inertial reference frame.
(b) An Inertial frame is either at rest or moving with uniform velocity.
(c) Frame moving at constant velocity relative to a known inertial frame is also an inertial frame.
(d) In an Inertial frame an object subject to zero net force will stay at rest or more at constant velocity.
(e) If acceleration of a particle is zero in one inertial frame, it is zero in all inertial frames.
(f) Idealy, no inertial frame exists in the universe for practical purpose, a frame of reference may be considered as Inertial if its acceleration is negligible with respect to the acceleration of the object to be observed.
Note :
(i) To measure the acceleration of a falling apple, earth can be considered as an inertial frame.
(ii) On the contrasy, to observe the motion of planets earth can not be considered as an inertial frame but for this purpose the Sun may be assumed an inertial frame.
4.2 Non Inertial Frame :
(i) An accelerated frame of reference is called a non inertial frame. Objects in non inertial frames do not obey Newton’s first Law.
(ii) Pseudo Force : Imaginary force which is recognised only by a non-Inertial observer to explain the physical situation according to Newton’s Laws.
(iii) Magnitude of pseudo force Fpis equal to the product of the mass m of the object and the acceleration a of the frame of reference.
(iv) The direction of the force is opposite to the direction of acceleration. Fp = –ma
(v) Force is imaginary in the sense that it has no physical origin, that is, it is not caused by one of the basic interactions in nature. It does not exist in the action reaction pair.

A ball is dropped inside a car which is initially at rest but has an acceleration a to the right.
(i) A stationary observer on the ground observes that the ball is falling vertically downwards with an acceleration g (downwards) (i) A person in the accelerated car observes that the ball moves down and towards the left of the car
(ii) Horizontally the ball does not move only the car moves to the right.(ii) According to this observer, the backward acceleration of the ball is caused by the pseudo force.
Example: A block of mass m rests on a smooth horizontal surface. It is being observed by two observers A and B ; observer A is stationary on the ground, observer B rides on a car moving towards right with an acceleration a. Draw the free body diagrams (F.B.D.) of the block as observed by A and B.

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