能量

機械能

作功

${\displaystyle W=\mathbf {F} \cdot \Delta \mathbf {r} \,}$，或者寫做
${\displaystyle W=m\mathbf {a} \,\cdot \Delta \mathbf {r} \,}$

${\displaystyle W=\int _{C}\mathbf {F} (\mathbf {r} )\cdot \mathrm {d} \mathbf {r} \,}$

動能

{\displaystyle {\begin{aligned}v^{2}&=v_{0}^{2}+2a\left(r-r_{0}\right)\\\end{aligned}}}

${\displaystyle \mathbf {a} ={v^{2}-v_{0}^{2} \over 2\left(r-r_{0}\right)}}$，即係
${\displaystyle \mathbf {a} ={v^{2}-v_{0}^{2} \over 2\Delta \mathbf {r} }}$，跟住代呢條式落去功嗰條式（${\displaystyle W=m\mathbf {a} \,\cdot \Delta \mathbf {r} \,}$）嗰度嘅話就會出到
${\displaystyle W=m\Delta \mathbf {r} \cdot \,{v^{2}-v_{0}^{2} \over 2\Delta \mathbf {r} }}$，跟住一路執：
${\displaystyle W=m\cdot \,{v^{2}-v_{0}^{2} \over 2}}$
${\displaystyle W={{1 \over 2}mv^{2}}-{{1 \over 2}mv_{0}^{2}}}$

位能

${\displaystyle W=\mathbf {F} _{g}\Delta \mathbf {r} }$

${\displaystyle \mathbf {F} _{g}\Delta \mathbf {r} ={{1 \over 2}mv^{2}}}$

相關定律

第一定律

 「 一切嘅能量，形式可以轉化，但就唔能憑空產生，亦都唔會憑空消失。 」

${\displaystyle \Delta U=Q-W}$

註釋

1. Δr = rfinalrinitialrfinal 係件物體最後個位置，而 rinitial 係佢初頭個位置。

攷

1. Movement means energy 互聯網檔案館歸檔，歸檔日期2018年1月6號，..
2. Naito, K., Takagi, H., & Maruyama, T. (2011). Mechanical work, efficiency and energy redistribution mechanisms in baseball pitching. Sports Technology, 4(1-2), 48-64.
3. Conservative Force. HyperPhysics.
4. Bernoulli's Equation & Applications Of Bernoulli's Equation 互聯網檔案館歸檔，歸檔日期2020年3月16號，..
5. 引用錯誤 無效嘅<ref>標籤；無文字提供畀叫做ohanian嘅參照
6. Pendrill, A. M., Karlsteen, M., & Rödjegård, H. (2012). Stopping a roller coaster train. Physics Education, 47(6), 728.
7. Shaw, S. W., & Haddow, A. G. (1992). On 'roller-coaster' experiments for nonlinear oscillators. Nonlinear Dynamics, 3(5), 375-384.
8. Mandl, F. (1988) [1971]. Statistical Physics (2nd ed.). Chichester·New York·Brisbane·Toronto·Singapore: John Wiley & sons.