physics-ai999x

About this model

physics-ai999x answers physics questions written in everyday language — kinematics, forces, energy, momentum, rotation, waves, fluids, thermodynamics, electricity, magnetism and optics — with step-by-step working, units and LaTeX. It runs offline on any CPU as a Python package, with ONNX formula graphs for other languages and a compact ONNX model that reads free-form questions. Version 2 adds search across every AI999X model — ask in your own words and it points you to the right formula, even in another model — and figures of any answer, drawn in your notebook.

Install

pip install physics-ai999x
hf download AI999X/physics-ai999x --local-dir physics-ai999x

Use

import physics_ai999x as physics
physics.ask("A 3 kg object moves at 4 m/s. What is its kinetic energy?")
# -> 24 J, with the formula and the steps

Formulas

109 capabilities. Open any of them on the capability orb to solve it in your browser.

Show all 109 formulas

Angular velocity under constant angular acceleration

\omega = \omega_{0} + \alpha t

Average net force from a change of momentum

F = \frac{p_2 - p_1}{t}

Average power

P = \frac{E}{t}

Capacitance of parallel plates

C = \frac{\varepsilon_{0} A}{d}

Carnot (maximum) efficiency

\text{eff} = 1 - \frac{T_{c}}{T_{h}}

Centripetal acceleration

a = \frac{v^{2}}{r}

Centripetal acceleration from angular velocity

a = r \omega^{2}

Centripetal force

F = \frac{m v^{2}}{r}

Charge carried by a steady current

Q = I t

Charge on a capacitor

Q = C V

Coefficient of performance of a heat pump

\text{cop} = \frac{Q_{h}}{W}

Coefficient of performance of a refrigerator

\text{cop} = \frac{Q_{c}}{W}

Component of the weight along an incline

F = m g \sin\left(\theta\right)

Current dying away in an RL circuit

I = I_{0} e^{\frac{-t}{\tau}}

De Broglie wavelength

\lambda = \frac{h}{p}

Displacement from the mean of initial and final velocity

x = \frac{\left(v_0 + v\right) t}{2}

Displacement under constant acceleration

x = v_0 t + \frac{a t^{2}}{2}

Efficiency of a heat engine

\text{eff} = \frac{W}{Q_{h}}

Electric field of a point charge

E_{f} = \frac{k_{e} Q}{r^{2}}

Electric potential of a point charge

V = \frac{k_{e} Q}{r}

Electric power

P = V I

Emf of a rod moving through a magnetic field

\text{emf} = B l v

Energy balance of a cyclic heat engine

W = Q_{h} - Q_{c}

Energy of a photon

E = h f

Energy stored in a capacitor

\text{Ecap} = \frac{C V^{2}}{2}

Energy stored in a linear spring

U = \frac{k x^{2}}{2}

Flow rate as volume per time

Q = \frac{V}{t}

Flow rate through a cross section

Q = A v

Focal length of a spherical mirror

f = \frac{R}{2}

Force of a linear spring

F = k x

Force on a charge in an electric field

F = q E_{f}

Gravitational acceleration at a distance from a mass

g = \frac{G M}{r^{2}}

Gravitational potential energy near the surface

U = m g h

Heat for a temperature change

Q = m c \Delta T

Heat to boil or condense

Q = m L_{v}

Heat to melt or freeze

Q = m L_{f}

Ideal gas law

P V = n R T

Impulse of a constant force

J = F t

Index of refraction

n = \frac{c}{v}

Intensity as power per area

I = \frac{P}{A}

Linear momentum

p = m v

Linear thermal expansion

d_{L} = \alpha_{t} L d_{T}

Magnetic field at the centre of a circular loop

B = \frac{\mu_{0} I}{2 r}

Magnetic field inside a long solenoid

B = \mu_{0} n_{t} I

Magnetic field of a long straight wire

B = \frac{\mu_{0} I}{2 \pi r}

Magnetic force on a current-carrying wire

F = I L B \sin\left(\theta\right)

Magnetic force on a moving charge

F = q v B \sin\left(\theta\right)

Mass density

\rho = \frac{m}{V}

Maximum height of a vertical throw

h = \frac{v_0^{2}}{2 g}

Maximum speed of a mass on a spring

v = X \sqrt{\frac{k}{m}}

Momentum of a photon

p = \frac{h}{\lambda}

Motion at constant velocity

d = v t

Net force and acceleration

F = m a

Net force with an opposing friction force

F = P - f

Normal force on a level surface

N = W

Normal force on an incline

N = m g \cos\left(\theta\right)

Period and frequency

T = \frac{1}{f}

Period of a circular orbit

T = 2 \pi \sqrt{\frac{r^{3}}{G M}}

Period of a mass on a spring

T = 2 \pi \sqrt{\frac{m}{k}}

Period of a simple pendulum

T = 2 \pi \sqrt{\frac{L_{p}}{g}}

Photon energy from wavelength

E = \frac{h c}{\lambda}

Potential difference in a uniform field

V = E_{f} d

Power from current and resistance

P = I^{2} R

Power from voltage and resistance

P = \frac{V^{2}}{R}

Power of a force on a moving body

P = F v

Pressure of a column of fluid

P = \rho g h

Pressure of a force on an area

P = \frac{F}{A}

Radius of a charged particle's circle in a magnetic field

r = \frac{m v}{q B \sin\left(\theta\right)}

Reactance of a capacitor

X = \frac{1}{2 \pi f C}

Reactance of an inductor

X = 2 \pi f L

Resistance of a uniform wire

R = \frac{\rho_{e} L}{A}

Resonant frequency of an LC circuit

f = \frac{1}{2 \pi \sqrt{L C}}

Rest energy

E_{0} = m c^{2}

Rms current of a sinusoidal supply

I_{\text{rms}} = \frac{I_{0}}{\sqrt{2}}

Rms voltage of a sinusoidal supply

V_{\text{rms}} = \frac{V_{0}}{\sqrt{2}}

Rotational kinetic energy

K_{R} = \frac{I_{r} \omega^{2}}{2}

Sliding friction

f = \mu N

Speed after a displacement under constant acceleration

v^{2} = v_0^{2} + 2 a x

Speed after falling from rest

v = \sqrt{2 g h}

Speed in a circular orbit

v = \sqrt{\frac{G M}{r}}

Speed of a body launched by a spring

\frac{k x^{2}}{2} = \frac{m v^{2}}{2}

Speed of a periodic wave

v = f \lambda

Speed on a circle from angular speed

v = \omega r

Tangential acceleration of a point on a rotating body

a = r \alpha

Tension in a rope holding a hanging body

T = m g

Thermal expansion of an area

d_{A} = 2 \alpha_{t} A d_{T}

Thermal expansion of volume

d_{V} = \beta V_{0} d_{T}

Thin lens equation

\frac{1}{d_{o}} + \frac{1}{d_{i}} = \frac{1}{f}

Time constant of an RC circuit

\tau = R C

Time constant of an RL circuit

\tau = \frac{L}{R}

Time to the top of a vertical throw

t = \frac{v_0}{g}

Torque of a force

\tau = r F \sin\left(\theta\right)

Translational kinetic energy

K = \frac{m v^{2}}{2}

Two resistors in series and in parallel

r_{s} = r_{1} + r_{2},\quad r_{p} \left(r_{1} + r_{2}\right) = r_{1} r_{2}

Velocity and displacement after constant acceleration

v = u + a t,\quad 2 s = \left(u + v\right) t

Velocity under constant acceleration

v = v_0 + a t

Voltage across an ohmic resistance

V = I R

Voltage of a charging capacitor

V = \text{emf} \left(1 - e^{\frac{-t}{R C}}\right)

Voltage of a discharging capacitor

V = V_{0} e^{\frac{-t}{R C}}

Wavelength of light in a medium

\lambda_{n} = \frac{\lambda}{n}

Weight in a uniform gravitational field

W = m g

Work by a constant force

W = F d \cos\left(\theta\right)

Work-energy theorem

W = \frac{m \left(v^{2} - v_0^{2}\right)}{2}

Topics

• Physics
• Physics Solver
• Step By Step Solutions
• Homework Help
• Education
• Offline
• Feature Extraction
• Semantic Search
• Physics Calculator
• Kinematics

Versions

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