Enter the inertial mass, change in velocity, and change in time into the calculator to determine the (average) force associated with that acceleration via Newton’s second law, F = m·(Δv/Δt). In a non-inertial reference frame, the corresponding inertial (fictitious) force has the same magnitude but the opposite direction.
Inertia Force Formula
The following equation is used to calculate the force associated with an average acceleration over a time interval (Newton’s second law):
IF = IM \cdot \frac{\Delta v}{\Delta t}- Where IF is the force associated with the acceleration (N)
- IM is the inertial mass (kg)
- Δv is the change in velocity (m/s)
- Δt is the change in time (s)
To calculate this force, multiply the inertial mass by the average acceleration, where average acceleration is Δv/Δt. If you are working in a non-inertial reference frame and specifically want the inertial (fictitious) force used in dynamics, it has the same magnitude but points opposite the acceleration (often written Finertial = −m·a).
What is an Inertia Force?
Definition:
In classical mechanics, an inertial (inertia) force is a fictitious (pseudo) force introduced when analyzing motion from a non-inertial (accelerating or rotating) reference frame. It is proportional to mass and is directed opposite the acceleration used in that frame (commonly written Finertial = −m·a). Separately, inertia is the resistance of an object to changes in velocity; for everyday problems this resistance is quantified by the object’s mass.
How to Calculate Inertia Force?
Example Problem:
The following example outlines the steps and information needed to calculate the force associated with a change in velocity over a given time interval.
First, determine the inertial mass. In this example, the inertial mass is found to be 15 kg.
Next, determine the change in velocity. For this problem, the change in velocity is found to be 3 m/s.
Next, determine the change in time. In this case, the change in time is measured to be 2 seconds.
Finally, calculate using the formula above:
IF = IM · (Δv/Δt)
IF = 15 · (3/2)
IF = 22.5 N
If you are using the inertial (fictitious) force in a non-inertial frame, it has the same magnitude but opposite direction to the acceleration (so along the same axis it would be written as −22.5 N for this example if Δv/Δt is taken as positive).
FAQ
What is the difference between inertia force and gravitational force?
Gravitational force is a real interaction force between masses (near Earth it is commonly approximated as W = m·g). An inertial (inertia) force is a fictitious/pseudo force introduced when working in a non-inertial (accelerating/rotating) reference frame; it is not a fundamental interaction and is used so that Newton’s laws can be applied in that non-inertial frame.
Can inertia force be negative?
Yes. The sign of any force component depends on your chosen coordinate convention. In particular, the inertial (fictitious) force is defined to point opposite the acceleration used in the analysis (often written Finertial = −m·a), so along a given axis it will have the opposite sign of the corresponding acceleration component.
How does the mass of an object affect its inertia force?
For a given acceleration, the magnitude of the associated force scales linearly with mass: |F| = m·|a|. That is why more massive objects require larger forces to achieve the same change in velocity over the same time interval.
