Inertia, interaction and mass

After a push, a trolley keeps rolling even after the hand lets go. Why is a loaded trolley harder to speed up? Let us separate two questions: what allows an existing velocity to persist, and what determines its change?

The push has ended, but the trolley still moves. Motion therefore does not need a hand to keep acting. If other objects exert no action, or their actions balance, an object stays at rest or keeps the same velocity in both magnitude and direction. This is inertia. For our everyday experiments, we can describe it relative to Earth with enough accuracy for this course. Later we will see why a rapidly accelerating observer needs a more detailed account.

A real trolley does stop. Has it simply used up its motion? Try a smoother floor and better wheels: it rolls longer because friction and air resistance have less effect. Imagine removing them entirely. There would be no cause for slowing down, so velocity would stay constant. Inertia is neither a stored supply nor a separate backward force. It names the observed persistence of velocity when the actions balance.

Compress a spring between two trolleys and release it. Both start moving: we cannot describe the event as a change in only one trolley. In an interaction, each object acts on the other, and their velocities or shapes may change. Different responses do not necessarily mean different durations of action. Even during the same interval, one trolley can change its velocity more than the other. The properties of the objects matter too.

Push an empty trolley and a loaded one in the same way for the same time. Under the same overall action, the loaded trolley changes velocity less. An object's resistance to a change in velocity is its inertia; mass m measures that property. The SI unit is the kilogram, kg. Mass matters both when speeding up and when slowing down. A trolley with greater mass is harder both to set moving and to change the velocity it already has.

A large empty box may be easier to move than a small metal part. Size cannot replace a measurement of mass. To compare inertia through changes in velocity, keep the action and its duration the same and reduce other effects, such as unequal friction. If one trolley is pushed longer, its final velocity alone no longer gives a reliable comparison. Mass is not a name for any kind of ‘amount’: amount of substance is a different physical quantity, measured in moles.

Equal constant forces act for equal times. The first trolley's velocity changes by 1 m/s, and the second's by 3 m/s. Which trolley has greater mass?

The conditions of the action are the same, so we can compare the objects' responses.

A smaller change in velocity means greater inertia. The first trolley has the smaller change.

The first trolley has greater mass: under the same action for the same time, its velocity changes less.

Without an unbalanced action, velocity stays constant; stopping needs a physical cause.

Mass measures inertia: the same action for the same time changes the velocity of an object with greater mass less.

When comparing objects, control the action, time and other effects. Size alone cannot tell you mass.

We can relate mass to volume. The next lesson shows how density helps us compare materials.