Non-Inertial Systems and Apparent Forces

This section delves into non-inertial reference systems and the concept of apparent forces that arise in accelerating frames.

Definition: An apparent force is a force that is not produced by a physical interaction, but is observed in a non-inertial system due to the acceleration of the system itself.

The document explains that apparent forces can be measured but do not have a physical source.

Example: A non-inertial system could be one that is in accelerated rectilinear motion relative to an inertial system, with acceleration a_NI.

The principle of dynamics is applied to objects within non-inertial frames, showing how the total acceleration is the sum of the acceleration relative to the non-inertial frame and the frame's acceleration:

a = a_NI + a_rel

The concept of apparent weight is introduced, demonstrating how the perceived weight of an object can change in accelerating reference frames:

Highlight: Apparent weight = true weight ± apparent force

Various scenarios are explored, such as:

• Constant velocity motion (apparent weight equals true weight)
• Acceleration upward (apparent weight greater than true weight)
• Acceleration downward (apparent weight less than true weight)
• Free fall (apparent weight becomes zero)

The centrifugal force is discussed as a specific type of apparent force in rotating reference frames:

Formula: Centrifugal force F_c = mω²r, where m is mass, ω is angular velocity, and r is radius of rotation

The document concludes with practical examples, such as the behavior of a smartphone in a turning vehicle, to illustrate the effects of apparent forces in everyday situations.

Example: A smartphone in a turning car appears to move outward due to the apparent centrifugal force, which is equal and opposite to the real centripetal force keeping it in circular motion.