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Theoretical Models

This section focuses on the general equations and laws that GamePhysics is based on.

Newton’s second law of motion

Refname	TM:NewtonSecLawMot
Label	Newton’s second law of motion
Equation	$\boldsymbol{F}=m\,\boldsymbol{a}\text{(}t\text{)}$
Description	$\boldsymbol{F}$ is the force ( ${\text{N}}$ ) $m$ is the mass ( ${\text{kg}}$ ) $\boldsymbol{a}\text{(}t\text{)}$ is the acceleration ( $\frac{\text{m}}{\text{s}^{2}}$ )
Notes	The net force $\boldsymbol{F}$ on a body is proportional to the acceleration $\boldsymbol{a}\text{(}t\text{)}$ of the body, where $m$ denotes the mass of the body as the constant of proportionality.
Source	–
RefBy	IM:transMot

Newton’s third law of motion

Refname	TM:NewtonThirdLawMot
Label	Newton’s third law of motion
Equation	${\boldsymbol{F}_{1}}=-{\boldsymbol{F}_{2}}$
Description	${\boldsymbol{F}_{1}}$ is the force exerted by the first body (on another body) ( ${\text{N}}$ ) ${\boldsymbol{F}_{2}}$ is the force exerted by the second body (on another body) ( ${\text{N}}$ )
Notes	Every action has an equal and opposite reaction. In other words, the force ${\boldsymbol{F}_{1}}$ exerted on the second rigid body by the first is equal in magnitude and in the opposite direction to the force ${\boldsymbol{F}_{2}}$ exerted on the first rigid body by the second.
Source	–
RefBy

Newton’s law of universal gravitation

Refname	TM:UniversalGravLaw
Label	Newton’s law of universal gravitation
Equation	$\boldsymbol{F}=G\,\frac{{m_{1}}\,{m_{2}}}{\|\boldsymbol{d}\|^{2}}\,\boldsymbol{\hat{d}}=G\,\frac{{m_{1}}\,{m_{2}}}{\|\boldsymbol{d}\|^{2}}\,\frac{\boldsymbol{d}}{\|\boldsymbol{d}\|}$
Description	$\boldsymbol{F}$ is the force ( ${\text{N}}$ ) $G$ is the gravitational constant ( $\frac{\text{m}^{3}}{\text{kg}\text{s}^{2}}$ ) ${m_{1}}$ is the mass of the first body ( ${\text{kg}}$ ) ${m_{2}}$ is the mass of the second body ( ${\text{kg}}$ ) $\|\boldsymbol{d}\|$ is the Euclidean norm of the distance between the center of mass of two bodies ( ${\text{m}}$ ) $\boldsymbol{\hat{d}}$ is the unit vector directed from the center of the large mass to the center of the smaller mass ( ${\text{m}}$ ) $\boldsymbol{d}$ is the distance between the center of mass of the rigid bodies ( ${\text{m}}$ )
Notes	Two rigid bodies in the universe attract each other with a force $\boldsymbol{F}$ that is directly proportional to the product of their masses, ${m_{1}}$ and ${m_{2}}$ , and inversely proportional to the squared distance ${\|\boldsymbol{d}\|^{2}}$ between them.
Source	–
RefBy	GD:accelGravity

Newton’s second law for rotational motion

Refname	TM:NewtonSecLawRotMot
Label	Newton’s second law for rotational motion
Equation	$\boldsymbol{τ}=\boldsymbol{I}\,α$
Description	$\boldsymbol{τ}$ is the torque ( $\text{N}\text{m}$ ) $\boldsymbol{I}$ is the moment of inertia ( $\text{kg}\text{m}^{2}$ ) $α$ is the angular acceleration ( $\frac{\text{rad}}{\text{s}^{2}}$ )
Notes	The net torque $\boldsymbol{τ}$ on a rigid body is proportional to its angular acceleration $α$ , where $\boldsymbol{I}$ denotes the moment of inertia of the rigid body as the constant of proportionality. We also assume that all rigid bodies involved are two-dimensional (from A:objectDimension).
Source	–
RefBy	IM:rotMot