Newton (unit)

Newton (unit). The newton, symbolized as N, is the SI derived unit of force. It is named in honor of the English mathematician and physicist Isaac Newton, whose laws of motion fundamentally describe the relationship between force and motion. One newton is defined as the force required to accelerate a mass of one kilogram at a rate of one metre per second squared.

Definition and derivation

The newton is derived directly from Newton's second law of motion, which states that the force acting on an object is equal to the mass of that object multiplied by its acceleration. This relationship, expressed as \(F = ma\), provides the foundational definition. Consequently, a force of one newton will impart an acceleration of one metre per second squared to a one-kilogram mass. This definition intentionally links the unit to the core SI base units of mass, length, and time, ensuring coherence within the International System of Units. The unit was officially adopted by the General Conference on Weights and Measures to create a standardized, universally applicable measure of force, replacing older systems like the kilogram-force.

Newton in SI base units

Expressed in terms of the seven SI base units, the newton is a composite unit. Its dimensional analysis yields the expression kilogram metre per second squared (kg⋅m⋅s⁻²). This breakdown highlights its dependence on the base units for mass (kilogram), length (metre), and time (second). This formulation ensures that all other derived units of force within the SI, such as the joule for energy or the pascal for pressure, maintain dimensional consistency. The coherence of the SI means that equations like the calculation of weight (\(W = mg\)) yield results in newtons without requiring additional conversion factors when using standard units.

Common multiples and submultiples

For practical measurement across vastly different scales, standard SI prefixes are used with the newton. Large forces are often expressed in kilonewtons (kN, 10³ N), meganewtons (MN, 10⁶ N), or giganewtons (GN, 10⁹ N), commonly encountered in structural engineering, rocket engine thrust ratings, and tectonic plate force calculations. Conversely, smaller forces may be measured in millinewtons (mN, 10⁻³ N) or micronewtons (μN, 10⁻⁶ N), which are relevant in fields like microbiology (cellular forces) and precision spacecraft propulsion. The dyne, the unit of force in the CGS system, is equal to 10⁻⁵ newtons.

Examples and applications

Everyday experiences provide intuitive examples of the newton's magnitude. The gravitational force on a small apple (with a mass of about 102 grams) is approximately one newton. An average adult human exerts a force of roughly 700 newtons on the ground while standing. In technology, a typical jet engine on an Airbus A320 produces about 120,000 newtons of thrust. In science, the instrument known as an atomic force microscope measures forces in the nanonewton range to image surfaces. The Hubble Space Telescope uses fine guidance sensors that can detect forces as small as a few micronewtons.

Related units

Several other units of force are related to the newton through defined conversion factors. The kilogram-force (kp), once common in engineering, is defined as the force exerted by Earth's gravity on one kilogram and is equal to about 9.80665 N. The pound-force (lbf), a unit in the US customary and imperial systems, is approximately 4.44822 N. The dyne, from the CGS system, is 10⁻⁵ N. Furthermore, the newton is the foundational unit for other derived SI units; for instance, the pascal (Pa) is one newton per square metre, and the joule (J) is one newton-metre.

Category:SI derived units Category:Units of force