Key Points

A force is a push or pull that can change an object's state of motion, its direction of motion, or its shape and size. An unbalanced force is required to change an object's velocity.

Balanced forces are equal in magnitude and opposite in direction, resulting in zero net force and no change in the state of motion. An unbalanced force causes a change in motion, meaning it produces acceleration.

An object remains in a state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force. This law is also known as the law of inertia.

Inertia is the natural tendency of an object to resist a change in its state of motion or rest. The mass of an object is the quantitative measure of its inertia; objects with greater mass have greater inertia.

Momentum ($p$) is the product of an object's mass ($m$) and its velocity ($v$). The formula is $p = m \times v$. Its SI unit is kilogram-meter per second ($\text{kg m s}^{-1}$).

The rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force. This law quantifies the relationship between force, mass, and acceleration.

Force ($F$) equals the product of mass ($m$) and acceleration ($a$). The formula is $F = m \times a$. This is the most common mathematical form of Newton's second law.

The SI unit of force is the newton, symbolized by N. One newton is the force that produces an acceleration of $1 \text{ m s}^{-2}$ on an object of mass $1 \text{ kg}$. Therefore, $1 \text{ N} = 1 \text{ kg m s}^{-2}$.

The change in momentum is given by $\Delta p = mv - mu$. According to the second law, the applied force is $F = \frac{mv - mu}{t}$, which shows that force is the rate of change of momentum.

To reduce the impact of a force, the time of impact is increased. Since $F = \frac{\Delta p}{t}$, increasing time ($t$) for the same change in momentum ($\Delta p$) decreases the force ($F$). This is used when catching a cricket ball or in high jump pits.

To every action, there is an equal and opposite reaction. These two forces act on different objects, are equal in magnitude, and opposite in direction.

Action and reaction forces always act on two different bodies. They never act on the same body, and therefore, they do not cancel each other out. For example, a gun recoils because the force on the bullet is matched by an equal and opposite force on the gun.