Non-Inertial Frames of Reference. Forces of Inertia

Non-inertial Frames of Reference. Forces of Inertia
Non-Inertial Frames of Reference
Forces of Inertia
Principle of Equivalence of Force of Gravity and Force of Inertia
Forces of Inertia in Rotating Frame of Reference
Centrifugal Force
Coriolis Force

Non-inertial Frames of Reference
The frame is called non-inertial one if it moves with acceleration relative to an inertial frame of reference.

Observer is in the Inertial Frame of Reference
2 forces: the of gravity, mg , and the tension of a thread, T .
The motion is described by the fundamental law of motion,

Observer is in the Non-Inertial Frame of Reference
The ball is in state of rest!
Newton’s law of motion seems to be not correct now!?

Non-Inertial Frames of Reference. Forces of Inertia
Non-Inertial Frames of Reference
Forces of Inertia
Principle of Equivalence of Force of Gravity and Force of Inertia
Forces of Inertia in Rotating Frame of Reference
Centrifugal Force
Coriolis Force

Observer is in the Non-Inertial Frame of Reference (cont.)
The force Fin. we call the force of inertia. But where does this force come from?

Frame Moves with Acceleration
In non-inertial system of reference an additional force - force of inertia - appears. Its magnitude is proportional to the acceleration of the moving frame of reference with respect to the inertial frame.

Forces of Inertia
- Forces of inertia exist in non-inertial frames of reference only, never forget it.
- As the forces of inertia are not the result of interaction of objects, the 3rd Newton’s law is not applicable to them.
- The magnitude of the force of inertia is proportional to the mass of the object.

Non-Inertial Frames of Reference. Forces of Inertia
Non-Inertial Frames of Reference
Forces of Inertia
Principle of Equivalence of Force of Gravity and Force of Inertia
Forces of Inertia in Rotating Frame of Reference
Centrifugal Force
Coriolis Force

Principle of equivalence of force of gravity and force of inertia
The principle of equivalence of gravitational and inertial mass lies at the heart of Einstein’s general theory of relativity.

Non-Inertial Frames of Reference. Forces of Inertia
Non-Inertial Frames of Reference
Forces of Inertia
Principle of Equivalence of Force of Gravity and Force of Inertia
Forces of Inertia in Rotating Frame of Reference
Centrifugal Force
Coriolis Force

Forces of Inertia in Rotating Frame of Reference
In frame the motion of the ball is uniform circular motion with . In K frame the motion of the ball is uniform circular motion, its velocity is .
The centripetal acceleration of the ball in K is
Multiplying by mass of the ball,

Centrifugal and Coriolis Forces
centrifugal force
force of Coriolis

Non-Inertial Frames of Reference. Forces of Inertia
Non-Inertial Frames of Reference
Forces of Inertia
Principle of Equivalence of Force of Gravity and Force of Inertia
Forces of Inertia in Rotating Frame of Reference
Centrifugal Force
Coriolis Force

Centrifugal Force
The centrifugal force of inertia causes difference in accelation due to gravity in different latitudes.