Published by Patrick Mutisya · 14 days ago
Understand that mass is the property of an object that resists change in motion (inertia).
An object remains at rest or moves with constant velocity unless acted upon by a net external force. The tendency to maintain its state of motion is called inertia, and the magnitude of inertia is measured by the object's mass.
The net force \$\mathbf{F}_{\text{net}}\$ on an object is proportional to the rate of change of its momentum:
\$\mathbf{F}_{\text{net}} = \frac{d\mathbf{p}}{dt}\$
For a body of constant mass this reduces to the familiar form:
\$\mathbf{F}_{\text{net}} = m\mathbf{a}\$
Here, \$m\$ is the inertial mass – the larger the mass, the smaller the acceleration produced by a given force.
For every action force there is an equal and opposite reaction force:
\$\mathbf{F}{AB} = -\mathbf{F}{BA}\$
This principle underlies the conservation of momentum in isolated systems.
Momentum is defined as the product of an object’s mass and its velocity:
\$\mathbf{p}=m\mathbf{v}\$
Because mass appears directly in the definition, a larger mass means a larger momentum for the same speed, and therefore a greater resistance to changes in motion.
In the absence of external forces, the total momentum of a closed system remains constant:
\$\sum \mathbf{p}{\text{initial}} = \sum \mathbf{p}{\text{final}}\$
This principle can be derived from Newton’s third law and is a powerful tool for analysing collisions.
Inertia is the qualitative description of an object’s resistance to a change in its state of motion. Quantitatively, inertia is expressed by the object's mass \$m\$. The larger the mass, the greater the force required to achieve a given acceleration, as shown by \$F = ma\$.
These problems highlight how mass governs the response of objects to applied forces and how momentum is conserved in interactions.
| Law | Mathematical Form | Physical Meaning | Role of Mass |
|---|---|---|---|
| Newton’s First Law | \$\mathbf{F}_{\text{net}} = 0 \;\Rightarrow\; \mathbf{v}= \text{constant}\$ | Objects maintain their state of motion unless acted upon. | Mass determines the amount of inertia resisting a change. |
| Newton’s Second Law | \$\mathbf{F}_{\text{net}} = m\mathbf{a}\$ | Force produces acceleration proportional to mass. | Mass is the proportionality constant linking force and acceleration. |
| Newton’s Third Law | \$\mathbf{F}{AB} = -\mathbf{F}{BA}\$ | Forces occur in equal and opposite pairs. | Mass of each body determines the resulting accelerations from the pair of forces. |
| Momentum Definition | \$\mathbf{p}=m\mathbf{v}\$ | Momentum combines mass and velocity into a conserved quantity. | Mass directly scales momentum, increasing resistance to change. |
| Conservation of Momentum | \$\sum \mathbf{p}{\text{initial}} = \sum \mathbf{p}{\text{final}}\$ | In an isolated system, total momentum remains constant. | Mass distribution among objects determines how momentum is shared after interactions. |