Combining only units of the three fundamental quantities of mechanics:

Units of Displacement (s), units of Net Force (f) and units of Time

(t), how many different ways - other than m = f/a = w/g - can you write

a mathematical definition for mass? I can come up with one to help get

things started:

First let's start with one of the simplest combiniations: Displacement

and time; to get what I call speed [s/t] - a rate of change in

position; where velocity is a combination of speed and direction; which

combination is useful to give an initial starting position and

direction of motion to a body of mass whose motion we wish to analysis:

A body with an initial velocity - rate of speed and direction [(s/t)i]

- will continue with this initial speed and direction until a net force

(f) is exerted upon, and/or by it; to change its speed and/or direction

from its original velocity [(s/t)i] to some other velocity [(s/t)t].

The algebraic change in this velocity, {from [(s/t)i] to [(s/t)t],}

divided by the period of time (t) that it takes is known as

acceleration {[(s/t)t]-[s/t)i]/t}. The quotient of a net force (f),

divided by the rate of change in velocity that it causes is a Constant;

called inertia; which is a measure of the quantity of matter - mass -

that is contained by the body. This constant can be written and/or

expressed mathematically: Commonly it is written as m = f/a.

Since a body's weight is the centripetal force exerted by it; on

Earth's surface or some other support thereon - like a weight-scale;

where the acceleration of free fall is called "g", and averages close

to 32 feet per second, per second, mass (m) is commonly written as w/g;

where, for any given body: f/a = w/g.

The common denominators here are the "a", and "g"; which can both be

written as: {[(s/t)t]-[s/t)i]/t}; so that f/{[(s/t)t]-[s/t)i]/t}, is

equal to w/{[(s/t)t]-[s/t)i]/t}.

Now that we have derived inertia, the measure of mass, as the quantity

of matter in a body of it; as being a combination of all three

fundamental quantities of mechanics: We are in a position to derive

the change in momentum as the product of its mass and its velocity (v),

as [wv/g].

We can also define energy. Whereas momentum is that property of a

moving mass which can give a moving body greater power; in proportion

to its speed, to act upon and displace other bodies:

Energy is the potential of a body to do work; either because of its

being stressed out of position, or out of its internally unstressed

configuration and the ability to relieve that stress, either through

returning to its former unstressed position, or unstressed

configuration: Sometimes with unimaginably, sudden vigor; like

explosions, nuclear reactions, nova and supernova.