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The concept of 'measure of matter' refers to the amount of substance present in an object, which we term as mass. Mass is a fundamental property of physical objects and is a measure of the resistance an object has to a change in its state of motion, also known as inertia. To say it simply, it helps us quantify how much 'stuff' is there in a given object.

For example, a sugar cube might have a mass of around 4 grams, whereas a textbook might have a mass closer to 1 kilogram. What's crucial to understand is that this mass is consistent regardless of where the object is located – whether on Earth, the moon, or in the vacuum of space. It is an intrinsic property of the object and is one of the key concepts in the study of physics, particularly when dealing with laws of motion and energy.

Distinguishing between scalar and vector quantities is pivotal in understanding physics. Scalars are quantities that are fully described by a magnitude alone. Examples include mass, time, and temperature – they do not require directionality to be fully described. Mass, the 'measure of matter', as discussed earlier, is a classic scalar quantity.

On the other hand, vector quantities are those that have both a magnitude and a direction. Forces are vector quantities, including weight, which is the force due to gravitational pull. When we say that an object weighs 10 Newtons downward, the 'downward' part signifies the direction, and the '10 Newtons' refers to the magnitude of the force.

Gravitational force is the pull that two bodies exert on each other. It is a fundamental interaction that causes objects with mass to be attracted to one another. On Earth, this force pulls objects towards the center of the planet, and it is what gives us weight. The gravitational force that an object experiences depends on its mass, the mass of the planet, and the distance between the object and the center of the planet.

Since the Earth is much more massive than objects on its surface, we typically just consider the object's mass and the acceleration due to Earth's gravity (approximately 9.81 meters per second squared) when calculating weight. Remarkably, this force not only governs the motion of planets and stars but also affects time and light, playing a central role in the general theory of relativity.

It's important to correctly use and distinguish between the units that represent mass and weight. Mass, the measure of matter within an object, uses units such as grams (g), kilograms (kg), and pounds (lb). These units are part of metric and imperial systems of measurement respectively, and they help us quantify the amount of material in an object.

On the flip side, weight, which is the force exerted by gravity on an object, is measured in Newtons (N), in the International System of Units (SI). The distinction between these units highlights the difference between mass and weight; the former relates to the inherent amount of matter, while the latter is about the gravitational pull on that matter. When solving problems in physics or simply discussing these concepts, using the correct unit underscores the understanding of whether we're referring to mass (a scalar) or weight (a vector).