It is perhaps one of the most important and typical item in physics.

To explain the existence of pseudo force we must first discuss on frame.

Reference Frame: The co-ordinate system that is used to locate the position of a body with reference to the body is known as reference frame.

            It is of two type:

Ex: any frame which is either stagnant or have a constant velocity only.

Ex: Circular track, a car with acc. etc Basically any frame with an acceleration

Necessity of Pseudo Force: To apply Newton?s law in a non inertial frame and thus to calculate the eqn of motion of the body or the system of body in the frame pseudo force is introduced on the system or the body.

REASON: The pseudo force is actually experienced in the same dynamic frame. It has no existence in another dynamic frame or in a static frame. For example if you r in a car and if it is accelerating then you will feel a pull from backside. It is nothing but the pseudo force. Considering the car as the dynamic frame the other passenger will also feel it as they are in the same dynamic frame. But a passerby on the static road will not feel this pull(pseudo force) as he is in a static frame. The passenger of another car with different acceleration will not be able to feel the same pseudo force as of yours as they are in different dynamic frame.

            So the main reason behind this pseudo force is inertia. As a body tries to continues in its state thus to balance the effective force on the frame a pseudo force in apparently applied on the body to explain the equilibrium of the body on the same dynamic frame.

1.      Pseudo force occurs due to inertia.

2.      As the inertia causes the body to continue in its state thus it always opposes the acc creating force

3.      Hence the pseudo force is also in the reverse direction of the effective or acc creating force on the frame.

4.      Thus on free body diagram of the body take a force ma where a=resultant acc of the frame and m=mass of the body in the reverse direction of the resultant acc of the frame.

1.      Man inside a lift: The diagram 1 shows the true diagram and the FBD of the lift and the man. As here pseudo is introduced thus for equilibrium

N= mg + ma

Here a can be ?ve or +ve depending on the motion of the lift

The similar eqn stands for pulley also.

2.      Pendulum inside a car: In the diagram 2 @=?.

Here also as pseudo is introduced thus for the equilibrium by using lammi?s theorem we write

ma/[sin(180+ ?)] = T/sin90 = mg/[sin(180- ?)]

      Hence the tension can now be calculated.

Let there be water inside a vessel with a constant acc a.

As water cannot withstand any shear thus the surface level of the water makes an angle of 90 with the resultant force.

The free body is shown in diagram3. Here ? = angle made by the surface with the horizon = angle made by the resultant force with mg where m = mass of any particle on the surface.

Therefore,

 tan? =   ma/mg = a/g.

As we all know in circular motion there is a radially inward centripetal force. This force on being acting on the frame it self a pseudo force here specially known as centrifugal force must be introduced to the body which is numerically equal to the centripetal force but acts in the opp direction. That is why when a body revolves round a planet it feels weightlessness as the gravitational pull between them is cancelled by the so called centrifugal force (of course in the same dynamic frame). By this method the eqn of motion can also be calculated.

                  THAT?S ALL FOLKS.

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