No, inertial force does not depend on the frame of reference, but displacement does. This fundamental difference has significant implications, particularly for concepts like work done, which varies across different frames.
Force and Frame of Reference
According to the principles of physics and as stated in the provided reference, "With change of frame of reference inertial force does not change." This means that real forces, such as gravity, tension, friction, or electromagnetic forces, which are responsible for accelerating objects, maintain the same magnitude and direction regardless of the inertial frame of reference from which they are observed.
- Inertial Forces: These are the forces that exist independently of the observer's motion. For example, the force of gravity acting on an apple is the same whether you are standing still, walking, or riding in a uniformly moving car.
- Non-Inertial (Pseudo) Forces: It's important to distinguish that while inertial forces are frame-independent, pseudo-forces (like centrifugal force or Coriolis force) appear in non-inertial (accelerating) frames of reference. These are not real interactions but rather apparent forces introduced to explain motion in such frames. The reference specifically states "inertial force," which refers to the fundamental forces.
Displacement and Frame of Reference
In contrast to force, "displacement may change" with a change of frame of reference. Displacement is a vector quantity representing the shortest distance from the initial to the final position of an object, along with its direction. Its value is entirely dependent on the chosen reference point (the origin of the coordinate system) and the observer's motion.
- Example: Imagine a person walking towards the front of a moving train.
- From the perspective of another passenger inside the train (their frame of reference): The person's displacement is simply the distance they walked relative to the train's floor.
- From the perspective of an observer standing on the ground (their frame of reference): The person's displacement is the distance they walked relative to the train's floor plus the distance the train moved relative to the ground during that time.
- Clearly, the displacement observed by the passenger is different from that observed by the ground observer.
Impact on Work Done
The dependency of displacement on the frame of reference, while force remains invariant (for inertial forces), directly affects the calculation of work done. The reference explicitly states: "So the work done by a force will be different in different frames."
Work (W) is defined as the dot product of force (F) and displacement (d): W = F ⋅ d. Since force (F) is constant but displacement (d) can vary between frames, the calculated work done will also vary. This is a crucial concept in understanding energy transfer in different systems.
Summary Table: Frame Dependency
To summarize the relationship between force, displacement, and their dependency on the frame of reference:
| Concept | Dependency on Frame of Reference | Explanation |
|---|---|---|
| Inertial Force | No | Real forces (like gravity, friction) are invariant across different inertial frames. |
| Displacement | Yes | The change in position of an object depends on the chosen reference point and the observer's motion. |
| Work Done | Yes | As work is a product of force and displacement, its value changes if displacement changes between frames. |
