# newton

##### SI coherent derived unit with special name and symbol
Name Symbol Derived quantity Expressed in terms of SI base units
newton N force kg m s-2

### Definition

The newton, symbol N, is the SI coherent derived unit of force.

One newton is the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force.

The newton is named after the English physicist Sir Isaac Newton (1643 – 1727).

### Force

A force is any interaction that, when unopposed, will change the motion of an object. A net force applied to an object with mass will cause the object to change its velocity, or accelerate. A force has both magnitude and direction, making it a vector quantity.

### Newton’s second law of motion

Newton’s second law of motion states that the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force.

The law can also be stated in terms of an object’s acceleration. For a constant-mass system, the net force, F, applied to an object of mass, m, is directly proportional to the product of the object’s mass, m, and its acceleration, a.

$F \propto ma$

Using SI coherent units, the proportionality constant is 1. Thus:

$F = ma$

where:

• F is the net force applied in newtons, symbol N,
• m is the mass of the object in kilograms, symbol kg,
• a is the object’s acceleration measured in metres per second squared, symbol m s-2.

$1 \ \text{N} = 1 \ \text{kg} \ \text{m} \ \text{s}^{-2}$

### Newton’s law of universal gravitation

Newton’s law of universal gravitation states that every point mass attracts every other point mass by a force acting along the line intersecting the two points. The force is directly proportional to the product of the two masses, and inversely proportional to the square of the distance between them.

$F \propto \dfrac{m_1 m_2} {r^2}$

Using SI coherent units, the proportionality constant is the gravitational constant, Thus:

$F = G \ \dfrac{m_1 m_2} {r^2}$

where:

• F is the gravitational force acting between the two objects, measured in newtons, symbol N,
• G is the gravitational constant, equal to 6.674 30(15) × 10-11 kg-1 m3 s-2,
• m1 and m2 are the masses of the two objects, measured in kilograms, symbol kg,
• r is the distance between the two objects, measured in metres, symbol m.

### Coulomb’s law

Coulomb’s law states that there is a force of attraction or repulsion acting along a straight line between two point charges. The force is directly proportional to the product of the two charges, and inversely proportional to the square of the distance between them. For like charges, the force is one of repulsion, for opposite charges the force is one of attraction.

$F \propto \dfrac{q_1 q_2}{r^2}$

Using SI coherent units, the proportionality constant is the Coulomb constant, Thus:

$F = k_e \ \dfrac{q_1 q_2} {r^2}$

where:

• F is the electrostatic force acting between the two charges, measured in newtons, symbol N,
• ke is the Coulomb constant, equal to approximately 8.987 551 792 × 109 N m2 C-2,
• q1 and q2 are the magnitudes of the two charges, measured in coulombs, symbol C,
• r is the distance between the two charges, measured in metres, symbol m.