Physics essentials: 50 laws and formulas

All 50 cards

1. 1
   Newton’s first law
   An object stays at rest or keeps moving at constant velocity unless a net external force acts on it

   Also called the law of inertia.
2. 2
   Newton’s second law
   $\vec{F}_{\text{net}} = m\vec{a}$

   Force is measured in newtons: $1\ \mathrm{N} = 1\ \mathrm{kg\,m/s^2}$.
3. 3
   Newton’s third law
   When A exerts a force on B, B exerts an equal and opposite force on A

   The two forces act on different objects, so they don’t cancel.
4. 4
   Velocity under constant acceleration
   $v = v_0 + at$
5. 5
   Displacement under constant acceleration
   $s = v_0 t + \tfrac{1}{2}at^2$
6. 6
   Constant-acceleration equation without time
   $v^2 = v_0^2 + 2as$
7. 7
   Gravitational acceleration at Earth’s surface
   $g \approx 9.81\ \mathrm{m/s^2}$
8. 8
   Weight
   $W = mg$

   Mass is the same everywhere; weight depends on the local gravitational field.
9. 9
   Momentum
   $\vec{p} = m\vec{v}$

   The total momentum of a system is conserved when no external force acts on it.
10. 10
    Impulse
    $J = F\,\Delta t = \Delta p$

    Why airbags help: a longer stopping time means a smaller force for the same change in momentum.
11. 11
    Kinetic friction force
    $f_k = \mu_k N$

    $N$ is the normal force. Static friction can rise up to $\mu_s N$ before an object slips.
12. 12
    Centripetal acceleration and force
    $a_c = \dfrac{v^2}{r}$, so $F_c = \dfrac{mv^2}{r}$

    Both point toward the center of the circle.
13. 13
    Newton’s law of universal gravitation
    $F = G\dfrac{m_1 m_2}{r^2}$

    $G \approx 6.674 \times 10^{-11}\ \mathrm{N\,m^2/kg^2}$
14. 14
    Torque
    $\tau = rF\sin\theta$

    $\theta$ is the angle between the lever arm and the force.
15. 15
    Hooke’s law
    $F = -kx$

    $k$ is the spring constant; the minus sign means the force opposes the displacement.
16. 16
    Pressure
    $P = \dfrac{F}{A}$

    Measured in pascals: $1\ \mathrm{Pa} = 1\ \mathrm{N/m^2}$.
17. 17
    Pressure at a depth in a fluid
    $P = P_0 + \rho g h$

    $P_0$ is the pressure at the surface and $\rho$ the fluid’s density.
18. 18
    Archimedes’ principle
    The buoyant force equals the weight of the fluid displaced: $F_b = \rho_{\text{fluid}} V g$
19. 19
    Kinetic energy
    $E_k = \tfrac{1}{2}mv^2$
20. 20
    Gravitational potential energy near Earth’s surface
    $E_p = mgh$
21. 21
    Elastic potential energy of a spring
    $E = \tfrac{1}{2}kx^2$
22. 22
    Work done by a constant force
    $W = Fd\cos\theta$

    Measured in joules: $1\ \mathrm{J} = 1\ \mathrm{N\,m}$.
23. 23
    Work–energy theorem
    The net work done on an object equals its change in kinetic energy: $W_{\text{net}} = \Delta E_k$
24. 24
    Power
    $P = \dfrac{W}{t}$

    Measured in watts: $1\ \mathrm{W} = 1\ \mathrm{J/s}$. For a constant force, also $P = Fv$.
25. 25
    Conservation of energy
    Energy is never created or destroyed, only converted from one form to another; the total energy of an isolated system is constant
26. 26
    Elastic vs inelastic collisions
    Both conserve momentum; only elastic collisions also conserve kinetic energy

    In a perfectly inelastic collision the objects stick together.
27. 27
    Mass–energy equivalence
    $E = mc^2$
28. 28
    First law of thermodynamics
    $\Delta U = Q - W$

    $Q$ is the heat added to the system and $W$ the work done by it. Some textbooks write $\Delta U = Q + W$, with $W$ the work done on the system.
29. 29
    Heat needed to change an object’s temperature
    $Q = mc\,\Delta T$

    $c$ is the specific heat capacity; for water it is about $4.18\ \mathrm{kJ\,kg^{-1}\,K^{-1}}$.
30. 30
    Ohm’s law
    $V = IR$
31. 31
    Electric power
    $P = IV = I^2R = \dfrac{V^2}{R}$
32. 32
    Resistors in series
    $R_{\text{total}} = R_1 + R_2 + \cdots$

    The same current flows through each resistor.
33. 33
    Resistors in parallel
    $\dfrac{1}{R_{\text{total}}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots$

    Each has the same voltage across it, and the total is less than the smallest resistance.
34. 34
    Coulomb’s law
    $F = k\dfrac{q_1 q_2}{r^2}$

    $k = \dfrac{1}{4\pi\varepsilon_0} \approx 8.99 \times 10^9\ \mathrm{N\,m^2/C^2}$
35. 35
    Electric current
    $I = \dfrac{Q}{t}$

    Measured in amperes: $1\ \mathrm{A} = 1\ \mathrm{C/s}$.
36. 36
    Elementary charge
    $e \approx 1.602 \times 10^{-19}\ \mathrm{C}$

    The charge of a proton; an electron carries $-e$.
37. 37
    Capacitance
    $C = \dfrac{Q}{V}$

    Measured in farads. A capacitor stores energy $E = \tfrac{1}{2}CV^2$.
38. 38
    Kirchhoff’s circuit laws
    Current law: the current into a junction equals the current out (charge is conserved). Voltage law: the voltages around any closed loop sum to zero (energy is conserved)
39. 39
    Resistance of a wire
    $R = \rho\dfrac{L}{A}$

    $\rho$ is the material’s resistivity, $L$ the length and $A$ the cross-sectional area.
40. 40
    Faraday’s law of induction
    $\mathcal{E} = -\dfrac{d\Phi_B}{dt}$

    A changing magnetic flux induces an EMF. The minus sign is Lenz’s law: the induced current opposes the change that caused it.
41. 41
    Magnetic force on a moving charge
    $\vec{F} = q\vec{v} \times \vec{B}$

    Its magnitude is $qvB\sin\theta$. It is perpendicular to the velocity, so it does no work.
42. 42
    Wave speed, frequency and wavelength
    $v = f\lambda$

    Period and frequency are reciprocals: $T = \dfrac{1}{f}$.
43. 43
    Transverse vs longitudinal waves
    Transverse: the medium oscillates perpendicular to the direction of travel (waves on a string, light). Longitudinal: it oscillates along it (sound)
44. 44
    Speed of light in a vacuum
    $c = 299\,792\,458\ \mathrm{m/s} \approx 3.00 \times 10^8\ \mathrm{m/s}$

    Exact by definition: the metre is defined from it.
45. 45
    Speed of sound in air at 20 °C
    About $343\ \mathrm{m/s}$
46. 46
    Energy of a photon
    $E = hf = \dfrac{hc}{\lambda}$

    Planck constant $h \approx 6.626 \times 10^{-34}\ \mathrm{J\,s}$
47. 47
    Snell’s law
    $n_1 \sin\theta_1 = n_2 \sin\theta_2$

    Angles are measured from the normal to the surface.
48. 48
    Doppler effect
    The observed frequency rises when source and observer move toward each other and falls when they move apart

    It is why a passing siren drops in pitch.
49. 49
    Period of a simple pendulum
    $T = 2\pi\sqrt{\dfrac{L}{g}}$

    Valid for small swings; it doesn’t depend on the mass.
50. 50
    Period of a mass on a spring
    $T = 2\pi\sqrt{\dfrac{m}{k}}$