Physics

5.14 - Newton's 1st & 2nd Laws

7 min

Newton's first law

Resultant force and acceleration

Circular motion

F = ma

Inertia

note 1 of 4

Newton's First Law - Resultant force changes motion

Newton's First Law - If the resultant force on an object is zero, its velocity doesn't change:
- A stationary object stays stationary.
- A moving object continues at the same velocity (same speed and direction).
When an object is stationary or moving at a constant velocity, the forces on it are balanced.
Velocity only changes if the forces are unbalanced, giving a non-zero resultant force that causes an acceleration in the direction of the force.

Two cubes either side of a dashed line: the blue one labelled balanced has equal arrows pointing in from both sides, the orange one labelled unbalanced has a long arrow meeting a short one.

A non-zero resultant force can cause an object to:

start moving
stop moving
speed up
slow down
change direction

note 2 of 4

Newton's Second Law - Acceleration and resultant force

The larger the resultant force on an object, the more it accelerates - force and acceleration are directly proportional ( $F \propto a$ ).
Acceleration is inversely proportional to mass: for a fixed resultant force, a larger mass accelerates less than a smaller one.

Formula for Newton's Second Law

$F = m a$

Where:

$F$ = Resultant force, in newtons (N)
$m$ = Mass, in kilograms (kg)
$a$ = Acceleration, in metres per second squared (m/s²)

$F$ is always the resultant force, found by adding or subtracting the forces acting along the same line.

note 3 of 4

Worked example - Acceleration of a car

A car of mass 2,000 kg has an engine providing a driving force of 8,000 N. The drag force on the car is 2,000 N. Find its acceleration.

A purple car labelled 2,000 kg with a magenta arrow pointing left labelled 2,000 N and a longer orange arrow pointing right labelled 8,000 N.

Step 1 - Work out the resultant force

The driving force and drag force act along the same line in opposite directions, so subtract them.

$F = 8,000 - 2,000 = 6,000 N$

Step 2 - Rearrange F = ma for acceleration

$a = \frac{F}{m}$

Step 3 - Substitution and calculation

$a = \frac{6,000}{2,000} = 3 {m/s}^{2}$

The car accelerates at 3 m/s² in the direction of the resultant force.

note 4 of 4

Inertia and inertial mass

Inertia is the tendency of an object to continue in its current state of motion (at rest or moving at a constant velocity).
The larger an object's mass, the larger its inertia, and the harder it is to change its velocity.

Inertial mass

An object's inertial mass measures how difficult it is to change its velocity.
It's defined as the ratio of resultant force to acceleration:

$m = \frac{F}{a}$

key terms

TermDefinition

InertiaThe tendency of an object to stay at rest or to keep moving with uniform motion (at a steady speed in a straight line).

Inertial massA measure of how difficult it is to change an object's velocity, defined as the ratio of resultant force to acceleration.

end of notes

Key points to remember

Newton's First Law - Resultant force changes motion

Newton's First Law - If the resultant force on an object is zero, its velocity doesn't change:

A stationary object stays stationary.
A moving object continues at the same velocity (same speed and direction).

When an object is stationary or moving at a constant velocity, the forces on it are balanced.

Velocity only changes if the forces are unbalanced, giving a non-zero resultant force that causes an acceleration in the direction of the force.

Newton's Second Law - Acceleration and resultant force

The larger the resultant force on an object, the more it accelerates - force and acceleration are directly proportional (

F \propto a

Acceleration is inversely proportional to mass: for a fixed resultant force, a larger mass accelerates less than a smaller one.

Formula for Newton's Second Law

$F = m a$

Where:

F

= Resultant force, in newtons (N)

m

= Mass, in kilograms (kg)

a

= Acceleration, in metres per second squared (m/s²)

F

is always the resultant force, found by adding or subtracting the forces acting along the same line.

Inertia and inertial mass

Inertia is the tendency of an object to continue in its current state of motion (at rest or moving at a constant velocity).

The larger an object's mass, the larger its inertia, and the harder it is to change its velocity.

Inertial mass

An object's inertial mass measures how difficult it is to change its velocity.

It's defined as the ratio of resultant force to acceleration:

$m = \frac{F}{a}$