Newton's Law of Gravitation
Earth and Space

Deeper into mass

Physics Narrative for 11-14 Supporting Physics Teaching

Mass is a subtle idea – here's an account of some of its subtleties

The definition of mass in terms of the amount of stuff is the one that is commonly used in school science. Strictly speaking, however, the amount of stuff or matter should be measured in moles.

For a physicist, the mass of an object is a measure of its reluctance to be accelerated by a given force. Thus a 1 kilogram mass has a certain resistance to being accelerated by a given force, and a 2 kilogram has double that reluctance.

We sometimes express this in terms of inertia, stating that a bigger mass has a greater inertia or reluctance to be accelerated. You might consider the inertia of a juggernaut lorry or a super-tanker ship. Both of these require huge forces to set them moving (to accelerate them from rest). Equally, both need huge forces to bring them to a halt once they are moving (to decelerate them). Both have a large mass and a large inertia.

The relationship between mass and reluctance to accelerate can be seen in Newton's second law of motion:

acceleration = forcemass

Which is sometimes (although less helpfully) written as:

force = mass × acceleration

This equation allows you to predict that an object with a big mass will undergo a small acceleration if a given force is acting on it and vice versa.

So, although the physics definition of mass is in terms of resistance to acceleration, you can see that this measure is directly linked to the amount of stuff idea in that, the more matter or stuff there is in an object, the harder it is to set into motion, or stop.

Newton's Law of Gravitation
is expressed by the relation F=G(m_1)(m_2)/r^2
can be used to derive Kepler's First Law

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