## Force

• Force
Forces are also described as a push or pull on an object. They can be due to phenomena such as gravity, magnetism, or anything that might cause a mass to accelerate.
Common symbols
F, F
SI unit newton
In SI base units 1 kg·m/s2
Derivations from
other quantities
F = m a

In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.

The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object

Related concepts to force include: thrust, which increases the velocity of an object; drag, which decreases the velocity of an object; and torque, which produces changes in rotational speed of an object. In an extended body, each part usually applies forces on the adjacent parts; the distribution of such forces through the body is the so-called internal mechanical stress. Such internal mechanical stresses cause no accelation of that body as the forces balance one another. Pressure, the distribution of many small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate. Stress usually causes deformation of solid materials, or flow in fluids.

The four fundamental forces of nature
Property/Interaction Gravitation Weak Electromagnetic Strong
(Electroweak) Fundamental Residual
Acts on: Mass - Energy Flavor Electric charge Color charge Atomic nuclei
Particles experiencing: All Quarks, leptons Electrically charged Quarks, Gluons Hadrons
Particles mediating: Graviton
(not yet observed)
W+ W Z0 γ Gluons Mesons
Strength in the scale of quarks: 10−41 10−4 1 60 Not applicable
to quarks
Strength in the scale of
protons/neutrons:
10−36 10−7 1 Not applicable
20
Units of force
newton
(SI unit)
dyne kilogram-force,
kilopond
pound-force poundal
1 N ≡ 1 kg⋅m/s2 = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbf ≈ 7.2330 pdl
1 dyn = 10−5 N ≡ 1 g⋅cm/s2 ≈ 1.0197 × 10−6 kp ≈ 2.2481 × 10−6 lbf ≈ 7.2330 × 10−5 pdl
1 kp = 9.80665 N = 980665 dyn gn⋅(1 kg) ≈ 2.2046 lbf ≈ 70.932 pdl
1 lbf ≈ 4.448222 N ≈ 444822 dyn ≈ 0.45359 kp gn⋅(1 lb) ≈ 32.174 pdl
1 pdl ≈ 0.138255 N ≈ 13825 dyn ≈ 0.014098 kp ≈ 0.031081 lbf ≡ 1 lb⋅ft/s2
The value of gn as used in the official definition of the kilogram-force is used here for all gravitational units.

${\displaystyle {\vec {F}}={\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}},}$
${\displaystyle {\vec {F}}={\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}={\frac {\mathrm {d} \left(m{\vec {v}}\right)}{\mathrm {d} t}},}$
${\displaystyle {\vec {F}}=m{\frac {\mathrm {d} {\vec {v}}}{\mathrm {d} t}}.}$
${\displaystyle {\vec {F}}=m{\vec {a}}.}$
${\displaystyle {\vec {F}}_{1,2}=-{\vec {F}}_{2,1}.}$
${\displaystyle {\vec {F}}_{1,2}+{\vec {F}}_{\mathrm {2,1} }=0}$
${\displaystyle \sum {\vec {F}}=0.}$
${\displaystyle {\vec {F}}_{1,2}={\frac {\mathrm {d} {\vec {p}}_{1,2}}{\mathrm {d} t}}=-{\vec {F}}_{2,1}=-{\frac {\mathrm {d} {\vec {p}}_{2,1}}{\mathrm {d} t}}}$
${\displaystyle \Delta {{\vec {p}}_{1,2}}=-\Delta {{\vec {p}}_{2,1}}}$
${\displaystyle \sum {\Delta {\vec {p}}}=\Delta {{\vec {p}}_{1,2}}+\Delta {{\vec {p}}_{2,1}}=0}$,
${\displaystyle {\vec {F}}=\mathrm {d} {\vec {p}}/\mathrm {d} t}$
${\displaystyle {\vec {p}}={\frac {m_{0}{\vec {v}}}{\sqrt {1-v^{2}/c^{2}}}}}$
${\displaystyle v}$ is the velocity and
${\displaystyle c}$ is the speed of light
${\displaystyle m_{0}}$ is the rest mass.
${\displaystyle F_{x}=\gamma ^{3}ma_{x}\,}$
${\displaystyle F_{y}=\gamma ma_{y}\,}$
${\displaystyle F_{z}=\gamma ma_{z}\,}$
${\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}.}$
${\displaystyle F=ma}$
${\displaystyle F^{\mu }=mA^{\mu }\,}$
${\displaystyle {\vec {F}}=m{\vec {g}}}$
${\displaystyle {\vec {g}}=-{\frac {Gm_{\oplus }}{{R_{\oplus }}^{2}}}{\hat {r}}}$
${\displaystyle {\vec {F}}=-{\frac {Gm_{1}m_{2}}{r^{2}}}{\hat {r}}}$
${\displaystyle {\vec {E}}={{\vec {F}} \over {q}}}$
${\displaystyle B={F \over {I\ell }}}$
${\displaystyle {\vec {F}}=q({\vec {E}}+{\vec {v}}\times {\vec {B}})}$
${\displaystyle 0\leq F_{\mathrm {sf} }\leq \mu _{\mathrm {sf} }F_{\mathrm {N} }.}$
${\displaystyle F_{\mathrm {kf} }=\mu _{\mathrm {kf} }F_{\mathrm {N} },}$
${\displaystyle {\vec {F}}=-k\Delta {\vec {x}}}$
${\displaystyle {\frac {\vec {F}}{V}}=-{\vec {\nabla }}P}$
${\displaystyle {\vec {F}}_{\mathrm {d} }=-b{\vec {v}}\,}$
${\displaystyle b}$ is a constant that depends on the properties of the fluid and the dimensions of the object (usually the cross-sectional area), and
${\displaystyle \scriptstyle {\vec {v}}}$ is the velocity of the object.
${\displaystyle \sigma ={\frac {F}{A}}}$
${\displaystyle {\vec {\tau }}={\vec {r}}\times {\vec {F}}}$
${\displaystyle \scriptstyle {\vec {r}}}$ is the position vector of the force application point relative to the reference point.
${\displaystyle {\vec {\tau }}=I{\vec {\alpha }}}$
${\displaystyle I}$ is the moment of inertia of the body
${\displaystyle \scriptstyle {\vec {\alpha }}}$ is the angular acceleration of the body.
${\displaystyle {\vec {\tau }}={\frac {\mathrm {d} {\vec {L}}}{\mathrm {dt} }},}$ where ${\displaystyle \scriptstyle {\vec {L}}}$ is the angular momentum of the particle.
${\displaystyle {\vec {F}}=-{\frac {mv^{2}{\hat {r}}}{r}}}$
${\displaystyle {\vec {I}}=\int _{t_{1}}^{t_{2}}{{\vec {F}}\mathrm {d} t},}$
${\displaystyle W=\int _{{\vec {x}}_{1}}^{{\vec {x}}_{2}}{{\vec {F}}\cdot {\mathrm {d} {\vec {x}}}},}$
${\displaystyle {\text{d}}W\,=\,{\frac {{\text{d}}W}{{\text{d}}{\vec {x}}}}\,\cdot \,{\text{d}}{\vec {x}}\,=\,{\vec {F}}\,\cdot \,{\text{d}}{\vec {x}},\qquad {\text{ so }}\quad P\,=\,{\frac {{\text{d}}W}{{\text{d}}t}}\,=\,{\frac {{\text{d}}W}{{\text{d}}{\vec {x}}}}\,\cdot \,{\frac {{\text{d}}{\vec {x}}}{{\text{d}}t}}\,=\,{\vec {F}}\,\cdot \,{\vec {v}},}$
${\displaystyle {\vec {F}}=-{\vec {\nabla }}U.}$
${\displaystyle {\vec {F}}=-{\frac {Gm_{1}m_{2}{\vec {r}}}{r^{3}}}}$
${\displaystyle {\vec {F}}={\frac {q_{1}q_{2}{\vec {r}}}{4\pi \epsilon _{0}r^{3}}}}$
${\displaystyle {\vec {F}}=-k{\vec {r}}}$
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