Non - Inertial frame of reference :
The laws of physics do not change in their form if they are transferred from one inertial frame to another inertial frame. However if the frame of reference S' is accelerated with respect to S, then the basic laws become different. Such a frame of reference which is accelerated with respect to S is called the non - inertial frame of reference.
Fictitious force :
Consider S' the frame of reference is accelerating with an acceleration a0 with respect to another inertial frame S. If no force acts on a particle P, It has zero acceleration as observed by the person in frame S but the acceleration of P relative to it is -a0. It means that the observer in frame S' will observe that a force Fa= -ma0 acts on the particle P such a force which does not really act on a particle but appears to act due to acceleration of the frame is called Fictitious force.
F0 = -ma0
Consider an external force Fi acts on the particle P. The acceleration of the particle observed in the inertial frame S is ai. Therefore Fi = mai
The apparatus force F acting on the particle is observed in the non - inertial reference frame S'
F = Fi + F0
= mai + (-m a0)
Therefore fictitious force is that quantity which must be added to the real force acting on the particle in the inertial frame to give the value of apparant force in the non -inertial frame of reference
when mai = 0
F =F0 = -ma0
Here F0 is the fictitious force.
Examples :-
1) Centrifugal force :
Consider that a mass m is at rest in a non - inertial frame. From this frame the observed value of acceleration is a=0. Suppose the non -inertial frame is rotating with an angular velocity w about an axis fixed in an inertial frame.
Therefore a0 = -w^2r
This is the centripetal acceleration as observed in the inertial frame. The fictitious force,
F0 = -ma0
F0 = mw^2r
F0 is the centripetal force,
F = Fi + F0
= -mw^2r +mw^2r =0
Here -mw^2r is the centripetal force and mw^2r is the centrifugal force. The total observed force in the reference frame S is zero.
2) Freely falling bodies :
Consider an elevator falling freely under the action of gravity. It is a non - inertial frame of reference. If earth is the inertial frame of reference a0 = -gx
x is measured upwards from the surface of the earth, g is the acceleration due to gravity. The fictitious force F0 on a mass m in the following elevator is
F0 = -ma0 = mgx
Fi = -mgx + mgx = 0
It means, that the body is not accelerated in the elevator with respect to the falling elevator that is non - inertial frame in that case Fa = 0. It shows that the apparent weight of a body in the non - inertial frame of a freely falling elevator is zero. It also means weight tension.
If a body is in space of the elevator and has zero velocity with respect to the elevator it will remain suspended in space in the elevator when this is falling freely under gravity.
Special case :- If the elevator is moving downwards with the acceleration a0 where a0 < g.
F =Fi + F0
F = -mgx + ma0x
If the body is on the surface of the elevator in opposite weight
R = -F = m(g-ax)
If the elevator is moving up, the opposite weight
R= m(g+a0)..........................READ
Non - Inertia frame of reference CLICK HERE
CLICK HERE to join this website for free
The laws of physics do not change in their form if they are transferred from one inertial frame to another inertial frame. However if the frame of reference S' is accelerated with respect to S, then the basic laws become different. Such a frame of reference which is accelerated with respect to S is called the non - inertial frame of reference.
Fictitious force :
Consider S' the frame of reference is accelerating with an acceleration a0 with respect to another inertial frame S. If no force acts on a particle P, It has zero acceleration as observed by the person in frame S but the acceleration of P relative to it is -a0. It means that the observer in frame S' will observe that a force Fa= -ma0 acts on the particle P such a force which does not really act on a particle but appears to act due to acceleration of the frame is called Fictitious force.
F0 = -ma0
Consider an external force Fi acts on the particle P. The acceleration of the particle observed in the inertial frame S is ai. Therefore Fi = mai
The apparatus force F acting on the particle is observed in the non - inertial reference frame S'
F = Fi + F0
= mai + (-m a0)
Therefore fictitious force is that quantity which must be added to the real force acting on the particle in the inertial frame to give the value of apparant force in the non -inertial frame of reference
when mai = 0
F =F0 = -ma0
Here F0 is the fictitious force.
Examples :-
1) Centrifugal force :
Consider that a mass m is at rest in a non - inertial frame. From this frame the observed value of acceleration is a=0. Suppose the non -inertial frame is rotating with an angular velocity w about an axis fixed in an inertial frame.
Therefore a0 = -w^2r
This is the centripetal acceleration as observed in the inertial frame. The fictitious force,
F0 = -ma0
F0 = mw^2r
F0 is the centripetal force,
F = Fi + F0
= -mw^2r +mw^2r =0
Here -mw^2r is the centripetal force and mw^2r is the centrifugal force. The total observed force in the reference frame S is zero.
2) Freely falling bodies :
Consider an elevator falling freely under the action of gravity. It is a non - inertial frame of reference. If earth is the inertial frame of reference a0 = -gx
x is measured upwards from the surface of the earth, g is the acceleration due to gravity. The fictitious force F0 on a mass m in the following elevator is
F0 = -ma0 = mgx
Fi = -mgx + mgx = 0
It means, that the body is not accelerated in the elevator with respect to the falling elevator that is non - inertial frame in that case Fa = 0. It shows that the apparent weight of a body in the non - inertial frame of a freely falling elevator is zero. It also means weight tension.
If a body is in space of the elevator and has zero velocity with respect to the elevator it will remain suspended in space in the elevator when this is falling freely under gravity.
Special case :- If the elevator is moving downwards with the acceleration a0 where a0 < g.
F =Fi + F0
F = -mgx + ma0x
If the body is on the surface of the elevator in opposite weight
R = -F = m(g-ax)
If the elevator is moving up, the opposite weight
R= m(g+a0)..........................READ
Non - Inertia frame of reference CLICK HERE
CLICK HERE to join this website for free
No comments:
Post a Comment