التحليل الطيفي

A set of three physical laws forming the basis of classical mechanics. The first law (inertia) states an object remains at rest or in uniform motion unless acted upon by a net external force. The second law quantifies force as mass times acceleration, [latex]\vec{F} = m\vec{a}[/latex]. The third law states that for every action, there is an equal and opposite reaction.

A Newtonian fluid's shear stress is directly proportional to the rate of shear strain. This linear relationship is defined by Newton's law of viscosity: [latex]\tau = \mu \frac{du}{dy}[/latex], where [latex]\tau[/latex] is the shear stress, [latex]\mu[/latex] is the dynamic viscosity (a constant of proportionality), and [latex]\frac{du}{dy}[/latex] is the shear rate or velocity gradient.

Bernoulli's principle states that for an inviscid flow, an increase in a fluid's speed occurs simultaneously with a decrease in pressure or a decrease in its potential energy. It is a statement of the conservation of energy for a moving fluid, commonly expressed as [latex]p + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}[/latex] along a streamline.

ميكانيكا الموائع هي فرع من فروع الميكانيكا التطبيقية، تُعنى بدراسة سكون السوائل (السوائل الساكنة) وحركتها (السوائل المتحركة). تُطبّق ميكانيكا الموائع مبادئ أساسية للكتلة والزخم وحفظ الطاقة لتحليل سلوك الموائع والتنبؤ به. وتتنوع تطبيقاتها، من الديناميكا الهوائية والهيدروليكا إلى الأرصاد الجوية وعلم المحيطات.

قوة الطرد المركزي هي قوة قصور ذاتي أو "وهمية" تبدو مؤثرة على كتلة عند النظر إليها في إطار مرجعي دوار. تتجه هذه القوة شعاعيًا نحو الخارج انطلاقًا من محور الدوران. هذه القوة ليست تفاعلًا أساسيًا، بل تنشأ من قصور الجسم الذاتي، أي ميله للحفاظ على حركته في خط مستقيم في إطار قصور ذاتي.

Generalized Hooke's Law is the constitutive equation for linear elastic materials, stating that the stress tensor is linearly proportional to the strain tensor. The relationship is expressed as [latex]\sigma = C : \varepsilon[/latex], where [latex]\sigma[/latex] is the stress tensor, [latex]\varepsilon[/latex] is the strain tensor, and [latex]C[/latex] is the fourth-order stiffness tensor containing the material's elastic constants.

This law states that every particle attracts every other particle in the universe with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is [latex]F = G \frac{m_1 m_2}{r^2}[/latex], where [latex]G[/latex] is the gravitational constant. It unified terrestrial and celestial mechanics.

In an isolated system, the total momentum remains constant. An isolated system is one not subject to external forces. This principle follows from Newton's laws of motion. For a system of particles, the total momentum [latex]\vec{p}_{\text{total}} = \sum_{i} m_i \vec{v}_i[/latex] is conserved if the net external force is zero. This is fundamental to analyzing collisions.

In a reference frame rotating with an angular velocity [latex]\boldsymbol{\omega}[/latex], the centrifugal force [latex]\mathbf{F}_{\mathrm{cf}}[/latex] acting on an object of mass [latex]m[/latex] at a position vector [latex]\mathbf{r}[/latex] from the origin is given by the vector formula: [latex]\mathbf{F}_{\mathrm{cf}} = -m \boldsymbol{\omega} \times (\boldsymbol{\omega} \times \mathbf{r})[/latex]. This formula shows the force is directed perpendicular to the axis of rotation and outwards.