Inertia

Also called Inertial property

Inertia is a system's resistance to a change in its velocity. Mass is the measure of it: the greater the mass, the smaller the acceleration a given net force produces.

Inertia is the reason a net force is needed to change a motion at all, and Newton's first law is the statement of it: if the net force on a system is zero, the velocity of that system remains constant.

Read that carefully. It does not say the system stops. Constant velocity includes constant magnitude and constant direction, so a system at rest and a system coasting at 6 m/s in a straight line are the same case. A skater carving a turn at a steady 6 m/s is not: her direction is changing, so something is pushing her sideways.

Mass is the measure. Inertia is not a separate quantity with its own units. Where it appears numerically is as the mm in

a⃗sys=F⃗netmsys\vec{a}_{\text{sys}} = \frac{\vec{F}_{\text{net}}}{m_{\text{sys}}}

so at fixed net force, doubling the mass halves the acceleration.

There is no inertial force. Nothing on a free-body diagram is labelled "inertia", and no arrow represents a tendency to keep moving. Inertia describes how the system responds to the arrows that are there. An arrow needs a second object exerting it, and inertia has no second object.

The rotational analogue is rotational inertia, which depends on the axis as well as the mass, and that is where the analogy stops being simple.

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