Skip to main content Contents Index Prev Up Next \(\newcommand{\val}{Val\text{00E9}ry}
\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R}
\newcommand{\cA}{{\mathcal{A}}}
\newcommand{\cB}{{\mathcal{B}}}
\newcommand{\cC}{{\mathcal{C}}}
\newcommand{\cD}{{\mathcal{D}}}
\newcommand{\cE}{{\mathcal{E}}}
\newcommand{\cF}{{\mathcal{F}}}
\newcommand{\cG}{{\mathcal{G}}}
\newcommand{\cH}{{\mathcal{H}}}
\newcommand{\cI}{{\mathcal{I}}}
\newcommand{\cJ}{{\mathcal{J}}}
\newcommand{\cL}{{\mathcal{L}}}
\newcommand{\cM}{{\mathcal{M}}}
\newcommand{\Pow}{{\mathbb{P}}}
\newcommand{\cP}{{\mathcal{P}}}
\newcommand{\cR}{{\mathcal{R}}}
\newcommand{\cS}{{\mathcal{S}}}
\newcommand{\cT}{{\mathcal{T}}}
\newcommand{\cU}{{\mathcal{U}}}
\newcommand{\cV}{{\mathcal{V}}}
\newcommand{\cW}{{\mathcal{W}}}
\newcommand{\cX}{{\mathcal{X}}}
\newcommand{\bze}{{\bf 0}}
\newcommand{\bA}{{\bf A}}
\newcommand{\ba}{{\bf a}}
\newcommand{\bha}{{\bf \hat{a}}}
\newcommand{\bB}{{\bf B}}
\newcommand{\bob}{{\bf b}}
\newcommand{\bhb}{{\bf \hat{b}}}
\newcommand{\bC}{{\bf C}}
\newcommand{\bc}{{\bf c}}
\newcommand{\bhc}{{\bf \hat{c}}}
\newcommand{\bD}{{\bf D}}
\newcommand{\bod}{{\bf d}}
\newcommand{\be}{{\bf \hat{e}}}
\newcommand{\bef}{{\bf \hat{f}}}
\newcommand{\bof}{{\bf f}}
\newcommand{\force}{{\bf f}}
\newcommand{\bF}{{\bf F}}
\newcommand{\tbF}{\tilde{\bf F}}
\newcommand{\bG}{{\bf G}}
\newcommand{\bog}{{\bf g}}
\newcommand{\bg}{{\bf g}}
\newcommand{\bH}{{\bf H}}
\newcommand{\bh}{{\bf h}}
\newcommand{\bI}{{\bf I}}
\newcommand{\bi}{{\boldsymbol{\hat{\imath}}}}
\newcommand{\bj}{{\boldsymbol{\hat{\jmath}}}}
\newcommand{\bk}{{\bf \hat{k}}}
\newcommand{\bK}{{\bf \hat{K}}}
\newcommand{\bL}{{\bf L}}
\newcommand{\bl}{\mathbfit{l}}
\newcommand{\bM}{{\bf M}}
\newcommand{\bn}{{\bf \hat{n}}}
\newcommand{\bq}{{\bf q}}
\newcommand{\conjQ}{\overline{Q}}
\newcommand{\conjP}{\bar{P}}
\newcommand{\bp}{{\bf p}}
\newcommand{\br}{{\bf r}}
\newcommand{\bs}{{\bf s}}
\newcommand{\bS}{{\bf S}}
\newcommand{\bR}{{\bf R}}
\newcommand{\bT}{{\bf T}}
\newcommand{\bt}{{\bf \hat{t}}}
\newcommand{\bu}{{\bf \hat{u}}}
\newcommand{\buu}{{\bf {u}}}
\newcommand{\bU}{{\bf U}}
\newcommand{\vel}{{\bf v}}
\newcommand{\bV}{{\bf V}}
\newcommand{\bv}{{\bf \hat{v}}}
\newcommand{\bvv}{{\bf {v}}}
\newcommand{\vv}{{\bf v}^*}
\newcommand{\bww}{{\bf {w}}}
\newcommand{\pvel}{{\bf w}}
\newcommand{\bW}{{\bf W}}
\newcommand{\bw}{{\bf \hat{w}}}
\newcommand{\bx}{{\bf \hat{x}}}
\newcommand{\bxx}{{\bf x}}
\newcommand{\bX}{{\bf X}}
\newcommand{\bY}{{\bf Y}}
\newcommand{\by}{{\bf \hat{y}}}
\newcommand{\byy}{{\bf y}}
\newcommand{\bz}{{\bf \hat{z}}}
\newcommand{\bom}{\boldsymbol{\omega}}
\newcommand{\bde}{\mathbf{\delta}}
\newcommand{\bOm}{\boldsymbol{\Omega}}
\newcommand{\bal}{\boldsymbol{\alpha}}
\newcommand{\bomFE}{{\boldsymbol{\omega}}_{\cF/\cE}}
\newcommand{\bomBA}{{\boldsymbol{\omega}}_{\cB/\cA}}
\newcommand{\bGa}{\boldsymbol{\Gamma}}
\newcommand{\btau}{\hat{\boldsymbol{\tau}}}
\newcommand{\rot}{\boldsymbol{\tau}}
\newcommand{\grad}{\boldsymbol{\nabla}}
\newcommand{\iner}{{\cal I}_B}
\newcommand{\inerG}{{\cal I}_G}
\newcommand{\Earth}{\text{Earth}}
\newcommand{\Arrow}{\mbox {$\longrightarrow$}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\al}{\alpha}
\newcommand{\ep}{\epsilon}
\newcommand{\ga}{\gamma}
\newcommand{\te}{\theta}
\newcommand{\la}{\lambda}
\newcommand{\om}{\omega}
\newcommand{\Om}{\Omega}
\newcommand{\ro}{\rho}
\newcommand{\Si}{\Sigma}
\newcommand{\pSi}{{\partial \Sigma}}
\newcommand{\bSi}{{\bar{\Sigma}}}
\newcommand{\si}{\sigma}
\newcommand{\dl}{\dot{l}}
\newcommand{\ddl}{\ddot{l}}
\newcommand{\dep}{\dot{\ep}}
\newcommand{\ddep}{\ddot{\ep}}
\newcommand{\ddbe}{\ddot{\beta}}
\newcommand{\dbe}{\dot{\beta}}
\newcommand{\dal}{\dot{\alpha}}
\newcommand{\ddal}{\ddot{\alpha}}
\newcommand{\ddga}{\ddot{\gamma}}
\newcommand{\dphi}{\dot{\phi}}
\newcommand{\ddphi}{\ddot{\phi}}
\newcommand{\dpsi}{\dot{\psi}}
\newcommand{\ddpsi}{\ddot{\psi}}
\newcommand{\dte}{\dot{\te}}
\newcommand{\ddte}{\ddot{\te}}
\newcommand{\dom}{\dot{\om}}
\newcommand{\dx}{\dot{x}}
\newcommand{\ddx}{\ddot{x}}
\newcommand{\dX}{\dot{X}}
\newcommand{\ddX}{\ddot{X}}
\newcommand{\dy}{\dot{y}}
\newcommand{\ddy}{\ddot{y}}
\newcommand{\dY}{\dot{Y}}
\newcommand{\ddY}{\ddot{Y}}
\newcommand{\dz}{\dot{z}}
\newcommand{\dZ}{\dot{Z}}
\newcommand{\ddz}{\ddot{z}}
\newcommand{\ddZ}{\ddot{Z}}
\newcommand{\Dp}{\dot{p}}
\newcommand{\ddr}{\ddot{r}}
\newcommand{\dr}{\dot{r}}
\newcommand{\dq}{\dot{q}}
\newcommand{\dQ}{\dot{Q}}
\newcommand{\tq}{\tilde{q}}
\newcommand{\ddq}{\ddot{q}}
\newcommand{\dbq}{\dot{{\bf q}}}
\newcommand{\ddbq}{\ddot{{\bf q}}}
\newcommand{\dds}{\ddot{s}}
\newcommand{\ds}{\dot{s}}
\newcommand{\dro}{\dot{\ro}}
\newcommand{\ddro}{\ddot{\ro}}
\newcommand{\dv}{\dot{v}}
\newcommand{\du}{\dot{u}}
\newcommand{\bSi}{\overline{\Sigma}}
\newcommand{\coB}{\overline{{\cal B}}}
\newcommand{\kin}{\mathbb{K}}
\newcommand{\qQ}{{\mathbb{Q}}}
\newcommand{\pot}{{\mathbb{U}}}
\newcommand{\hal}{{\mathbb{H}}}
\newcommand{\lag}{{\mathbb{L}}}
\newcommand{\gib}{{\mathbb{S}}}
\newcommand{\energ}{{\mathbb{E}}}
\newcommand{\danger}{\text{⚠}}
\newcommand{\ddanger}{\text{⚠}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Chapter 12 Power, Work & Energy
The notions of power, work and energy play a fundamental role in mechanics. After reviewing these concepts for forces acting on particles, we extend them to the case of mechanical actions exerted on rigid bodies. We can then relate power and kinetic energy by a straightforward application of the Principle of Virtual Power. We obtain a theorem of great practical importance, known as the Kinetic Energy Theorem (KET). The KET provides a single scalar equation, and, contrary to the Fundamental Theorem of Dynamics of the Newton-Euler formalism, requires the contribution of internal interactions between rigid bodies.
