Inertial Mass
Inertial Mass is a measure of an object's resistance to change in motion (acceleration) when a force is applied. Inertial mass determines how strongly an object resists acceleration
Inertial Mass appears directly in Newton's second law:
\[\mathbf{F} = m \cdot \mathbf{a}\]
where
- \[\mathbf{F} \text{ is the applied force,}\]
- \[m \text{ is the inertial mass, and}\]
- \[\mathbf{a} \text{ is the resulting acceleration.}\]
Or, we could say
- \[\mathbf{F} \text{ is the resulting force,}\]
- \[m \text{ is the inertial mass, and}\]
- \[\mathbf{a} \text{ is the applied acceleration.}\]
Or, from the perspective that acceleration is a function of Force
\[\mathbf{a} = \frac{\mathbf{F}}{m}\]
where
- \[\mathbf{a} \text{ is the resulting acceleration.}\]
- \[\mathbf{F} \text{ is the applied force, and}\]
- \[m \text{ is the inertial mass}\]
If the same force is applied to two objects, the object with greater inertial mass accelerates less. For example, pushing a 1 kg cart is easier to accelerate than a 100 kg cart because the 100 kg cart has much greater inertial mass.
Mass is a scalar. Mass is a derived quantity:
\[\require{physics} m= \frac{\abs{\mathbf{F}}}{\abs{\mathbf{a}}}\]
The word inertial comes from inertia: the tendency of an object to resist a change in its state of motion.
It is useful to distinguish inertial mass from gravitational mass
- Gravitational mass determines how strongly an object participates in gravity;
- Inertial mass determines how strongly it resists acceleration.
Experimentally, they they have been measured to extraordinary precision. These precise measurements provide a foundational observation behind Einstein's general theory of relativity.