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Savchenko Formulas

Name: Savchenko Formulas
License: https://creativecommons.org/licenses/by-sa/4.0/

Every formula the solutions on this site use for Savchenko's problems. Each card appears in at least one statement, solution or answer, 385 formulas in 1587 problems in all. Chapters and sections follow the book, and within a section the most used come first. Rest the cursor on a problem number to see its statement. Found a gap or a mistake, propose an edit.

Used most

1 $m\vec a = \sum \vec F$ Newton's second law2.1 Newton's laws 103 problems
2 $a_n = \frac{v^2}{R} = \omega^2 R$ Centripetal acceleration1.3 Motion in gravity field. Curvilinear motion 73 problems
3 $E_k = \frac{mv^2}{2} = \frac{p^2}{2m}$ Kinetic energy2.3 Kinetic energy. Work. Potential energy 65 problems
4 $F = \frac{1}{4\pi\varepsilon_0}\,\frac{q_1 q_2}{r^2} = k\,\frac{q_1 q_2}{r^2}$ Coulomb's law6.1 Coulomb's law. Electric field 51 problems
5 $\omega = \frac{d\varphi}{dt} = \frac{2\pi}{T} = 2\pi\nu, \qquad v = \omega R$ Angular velocity and period1.3 Motion in gravity field. Curvilinear motion 48 problems
6 $$x = x_0 + vt$$ Uniform motion1.1 Constant-speed motion 46 problems
7 $уповерхностипроводника$E = \frac{\sigma}{2\varepsilon_0}, \qquad E = \frac{\sigma}{\varepsilon_0}\ \text{(у поверхности проводника)}$$ Field of a charged plane6.2 The flux of the electric field. Gauss's theorem 45 problems
8 $x = A\cos(\omega t + \varphi_0), \qquad v = -A\omega\sin(\omega t + \varphi_0), \qquad a = -\omega^2 x$ Harmonic motion3.3 Harmonic motion 44 problems
9 $\vec E = \frac{\vec F}{q}, \qquad \vec F = q\vec E$ Field strength. Force on a charge6.1 Coulomb's law. Electric field 40 problems
10 $x = x_0 + v_0 t + \frac{at^2}{2}, \qquad v = v_0 + at$ Uniformly accelerated motion1.2 Variable-speed motion 38 problems
11 $\vec p = m\vec v, \qquad \Delta\vec p = \vec F\,\Delta t$ Momentum and impulse2.2 Momentum. Center of mass 38 problems
12 $тр$F_{\text{тр}} = \mu N$$ Sliding friction2.1 Newton's laws 37 problems
13 $m_1\vec v_1 + m_2\vec v_2 = m_1\vec v_1\,' + m_2\vec v_2\,'$ Conservation of momentum2.2 Momentum. Center of mass 37 problems
14 $A = \int \vec F\cdot d\vec r = Fs\cos\alpha$ Work of a force2.3 Kinetic energy. Work. Potential energy 37 problems
15 $$F = -kx$$ Hooke's law2.1 Newton's laws 36 problems
16 $C = \frac{\varepsilon\varepsilon_0 S}{d}, \qquad E = \frac{U}{d} = \frac{q}{\varepsilon_0 S}$ Parallel-plate capacitor6.4 Capacitors 35 problems
17 $I = \sum m_i r_i^2$ Moment of inertia2.7 Rotation of a solid body 34 problems
18 $\sum \vec F = 0, \qquad \sum M = 0$ Equilibrium of a rigid body2.8 Statics 34 problems
19 $E = \frac{1}{4\pi\varepsilon_0}\,\frac{q}{r^2}, \qquad \vec E = \sum_i \vec E_i$ Field of a point charge6.1 Coulomb's law. Electric field 33 problems
20 $$E_p = mgh$$ Potential energy in gravity2.3 Kinetic energy. Work. Potential energy 32 problems
21 $внутр$\oint \vec E\cdot d\vec S = \frac{q_{\text{внутр}}}{\varepsilon_0}$$ Gauss's law6.2 The flux of the electric field. Gauss's theorem 32 problems
22 $qvB = \frac{mv^2}{R}, \qquad R = \frac{mv}{qB} = \frac{p}{qB}$ Radius of the circle in a magnetic field10.1 Motion in a homogeneous magnetic field 32 problems
23 $внеш$M\vec a_c = \sum \vec F_{\text{внеш}}$$ Motion of the centre of mass2.2 Momentum. Center of mass 31 problems
24 $\ddot x + \omega^2 x = 0$ The harmonic oscillator equation3.3 Harmonic motion 31 problems
25 $E = \frac{Q}{4\pi\varepsilon_0 r^2}\ (r > R), \qquad E = \frac{\rho r}{3\varepsilon_0}\ (r < R)$ Field of a charged ball and shell6.2 The flux of the electric field. Gauss's theorem 30 problems
26 $\gamma = \frac{1}{\sqrt{1 - \beta^2}}, \qquad \beta = \frac{v}{c}$ Lorentz factor14.2 The slowing down of time and the reduction in the size of bodies in motion; the Lorentz Transformations 30 problems
27 $C = \frac{q}{U}, \qquad q = CU$ Capacitance of a capacitor6.4 Capacitors 29 problems
28 $\sin\alpha \approx \tan\alpha \approx \alpha, \qquad \cos\alpha \approx 1 - \frac{\alpha^2}{2}$ Small angles0.1 Approximations 28 problems
29 $\vec v = \vec v\,' + \vec u$ Addition of velocities1.4 Galileo's transformations 28 problems
30 $m = \rho V$ Mass from density2.1 Newton's laws 28 problems