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1 Primary & Middle School Physics1–9 年级在线 2 High School Physics10–12 年级在线 3 University Physics — Year 1本科一年级在线 4 University Physics — Year 2本科二年级在线 5 University Physics — Year 3本科三年级在线

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1 Markets I: The Ecosystem and Exchange-Traded Markets市场在线 2 Markets II: Rates, FX and Credit市场在线 3 Markets III: Commodities, Energy and Crypto市场在线 4 Quantitative Methods方法在线 5 Derivatives and Volatility衍生品在线 6 Rates, Credit, XVA and Risk利率、信用与风险在线 7 Research Craft: Predictors, Backtests, Measurement, Portfolios研究在线 8 Strategies I: Equities and Futures策略在线 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desks策略在线 10 Microstructure and Execution交易执行在线 11 Market Making and High-Frequency Trading做市在线 12 Machine Learning for Markets机器学习在线 13 Low-Latency Software技术在线 14 Networks, Hardware and Trading Infrastructure技术在线 15 Research, Data and Risk Platforms技术在线 16 The Desk and the Firm公司运营在线 17 The Industry: Firms, Roles and Careers职业发展在线 18 Interviews I: Maths, Probability and Speed职业发展在线 19 Interviews II: Markets, Trading Games and the Final Round职业发展在线 20 Interviews III: Code职业发展在线

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Physics · 术语表

什么是 Dimension？

Definition 1.5 University Physics — Year 1 · 第 1 章 — Units, Dimensions, and Measurement

The dimension of a quantity $X$ , written $[X]$ , records how $X$ is built from the seven base quantities, independently of the units chosen: length $L$ , mass $M$ , time $T$ , electric current $I$ , temperature $\Theta$ , amount of substance $N$ , luminous intensity $J$ . A speed has dimension $[v] = L\,T^{-1}$ , a force $[F] = M\,L\,T^{-2}$ , an energy $[E] = M\,L^2\,T^{-2}$ . A quantity of dimension $1$ (an angle, a ratio, a refractive index) is dimensionless.

示例

Example 1.8 (The period of a pendulum)

A pendulum of length $\ell$ and mass $m$ swings in gravity $g$ . Suppose its period is $\tau = k\,\ell^\alpha m^\beta g^\gamma$ with $k$ dimensionless. Then $T = L^\alpha M^\beta (L T^{-2})^\gamma = L^{\alpha+\gamma} M^\beta T^{-2\gamma}$ , so $\beta = 0$ , $\gamma = -\tfrac12$ , $\alpha = \tfrac12$ :

\tau = k\sqrt{\ell/g} .

Without solving a single equation of motion: the mass drops out, and doubling the length multiplies the period by $\sqrt2$ . Dynamics (Chapter 14) will supply $k = 2\pi$ for small swings.

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