Classical Physics Vol. 2 Pixel Sticker Sheet

10 pixel-art physics stickers on one A5 (5.83″ × 8.27″) white kiss-cut sheet: Classical Physics Vol. 2. Every character below has its own sticker page with the full physics panel.

Magnara

A spinning ball moving through air is pushed sideways, toward the side where its surface moves with the airflow. That Magnus force, proportional to spin crossed with velocity, makes spinning balls curve.

F_M = α ω×v
F_M: Magnus force on the spinning ball (N); α: empirical coefficient (depends on size, spin regime, fluid) (kg); ω: spin angular-velocity vector (rad/s); v: centre-of-mass velocity through the air (m/s); m: mass of the ball (kg); b: linear drag coefficient (kg/s)

Meldea

Around 1859 Franz Melde tied a string to the prong of a tuning fork and pulled it taut (Ann. Phys. 185, 193, 1860). At the right tensions the string broke into steady standing waves, with nodes that stood still and loops that blurred. Change the tension and the number of loops jumps.

f = n√(T/μ)/(2L)
f: frequency of the string vibration (Hz); n: number of loops; T: tension (N); μ: mass per unit length (kg/m); L: length of the string (m)

Pendulux

A pendulum keeps swinging in a fixed plane while the Earth turns beneath it. The swing plane appears to rotate at the Earth's rotation rate times the sine of the latitude: once a sidereal day at the poles, and not at all on the equator.

ω_prec = Ω_⊕ sin φ
ω_(prec): rate at which the swing plane turns relative to the floor (clockwise seen from above in the Northern Hemisphere) (°/h); Ω_(oplus): Earth's rotation rate relative to the stars: one turn per sidereal day of 23.93 h (°/h); φ: latitude (°)

Spinwell

Angular momentum is moment of inertia times angular speed, and without an outside torque it stays constant. Pull your arms in and your moment of inertia drops, so you spin faster.

L = Iω
L: angular momentum about the spin axis (kg m² / s); I: moment of inertia about that axis (kg m²); ω: angular speed (rad/s); τ: external torque about the axis (N m)

Terminara

A falling object speeds up until air drag, which grows with the square of speed, balances its weight. From then on it falls at a steady terminal velocity, approaching it along a tanh curve.

m dv/dt = mg − ½ρC_dAv²
m: mass of the skydiver (here 80 kg) (kg); v: falling speed (m/s); t: time since leaving the plane, falling from rest (s); g: gravitational acceleration (m/s²); ρ: air density (here 1.225 kg/m^3, sea-level standard) (kg/m³); C_d A: drag coefficient times frontal area (here 0.45 m^2, belly-down) (m²)

Barkhausa

Magnetise a piece of iron slowly and smoothly and its magnetisation does not change smoothly. It grows in many tiny, sudden jumps as the walls between magnetic domains snag on defects and then snap free. Heinrich Barkhausen heard this in 1919 by winding a coil around the iron and amplifying the induced pulses into a telephone receiver: a crackle (“Zwei mit Hilfe der neuen Verstärker entdeckte Erscheinungen”, Physikalische Zeitschrift 20, 401, 1919). Each jump induces a small voltage pulse in the coil.

V = −N dΦ/dt
V: voltage induced in the pick-up coil (V); N: number of turns of the coil; Φ: magnetic flux through the coil (Wb); t: time (s)

Displacera

Ampère's law broke down at a charging capacitor: current flows in the wire but not across the gap. James Clerk Maxwell fixed it in 1861–65 by adding a term for the changing electric field in the gap, which makes a magnetic field just as a real current does (“A Dynamical Theory of the Electromagnetic Field”, Phil. Trans. 155, 459, 1865). With it, the equations predicted electromagnetic waves travelling at the speed of light.

J_d = ε₀ ∂E/∂t
J_d: displacement current density (A/m²); ε₀: permittivity of free space (F/m); ∂E/∂t: rate of change of the electric field (V m⁻¹ s⁻¹)

Faradra

In September 1845 Michael Faraday sent polarised light through a block of heavy lead-borate glass placed between the poles of a strong electromagnet, with the field along the beam. When the magnet was switched on, the plane of polarisation turned. It was the first experimental link between light and magnetism. He reported it in the Nineteenth Series of his Experimental Researches in Electricity (Phil. Trans. R. Soc. 136, 1, 1846). The rotation angle grows with the field and with the path length.

β = VBd
β: rotation angle of the plane of polarisation (rad); V: Verdet constant of the material (rad T⁻¹ m⁻¹); B: magnetic flux density along the beam (tesla, T); d: path length through the material (m)

Galvana

William Thomson, later Lord Kelvin, developed the mirror galvanometer around the 1858 transatlantic telegraph cable, whose signals were too faint for ordinary needles. A tiny mirror carrying small magnets hangs inside a coil; a current twists it slightly, and a beam of light reflected from it sweeps across a scale. By the law of reflection, turning a mirror by an angle θ turns the reflected beam by twice that angle.

beam deflection = 2θ
θ: rotation angle of the mirror (rad); 2θ: rotation angle of the reflected beam (rad)

Inertix

Spin a coil of wire fast and stop it suddenly: the free charges inside keep going for a moment, like passengers in a braking bus, and a pulse of current flows. Richard Tolman and Thomas Stewart measured it in 1916 (Phys. Rev. 8, 97). From the charge that flowed they got the carriers' charge-to-mass ratio, close to that of the electron, showing that current in metals is carried by electrons.

Q = (m/e) v₀ L / R
Q: charge that flows after stopping (C); m/e: mass-to-charge ratio of the carriers (kg/C); v₀: rim speed of the wire before stopping (m/s); L: length of the wire (m); R: resistance of the coil (Ω)