Your FREE AP Physics 1 Flashcards 2026 – 200+ Cards

A quantity with magnitude only and no direction — e.g. speed, distance, mass, time.

A quantity with both magnitude and direction — e.g. velocity, acceleration, force, displacement.

Distance is the total path length (scalar); displacement is the straight-line change in position with direction (vector).

Speed is how fast (scalar); velocity is speed with direction (vector).

Displacement divided by elapsed time: $\bar v = \dfrac{\Delta x}{\Delta t}$.

The rate of change of velocity: $a = \dfrac{\Delta v}{\Delta t}$. A vector.

$v = v_0 + at$ — final velocity from initial velocity, acceleration, and time.

$x = x_0 + v_0 t + \tfrac{1}{2}at^2$.

$v^2 = v_0^2 + 2a\,\Delta x$ — use when time is unknown.

$\bar v = \dfrac{v_0 + v}{2}$ when acceleration is constant.

Motion under gravity alone (no air resistance), with downward acceleration $g \approx 9.8\ \text{m/s}^2$.

$g \approx 9.8\ \text{m/s}^2$ near Earth's surface (often approximated as $10\ \text{m/s}^2$).

Gives the velocity at that instant.

Gives the acceleration.

Gives the displacement.

Gives the change in velocity.

Two-dimensional motion under gravity; horizontal and vertical components are analyzed independently.

Stays constant — there is no horizontal force (ignoring air resistance).

Free fall: accelerates downward at $g$, independent of horizontal motion.

Set vertical displacement to zero and solve the vertical kinematic equation for $t$.

The coordinate system from which motion is measured; velocities add relative to it.

The velocity of one object measured from another: $\vec v_{AB} = \vec v_A - \vec v_B$.

Velocity at a single instant — the slope of the tangent to the position-time graph.

Motion at constant velocity (zero acceleration), shown as a straight line on a position-time graph.

Acceleration opposite to the velocity direction; it slows an object down (deceleration) if it's moving forward.

$\Delta x = \bar v\, t = \dfrac{v_0+v}{2}\,t$.

A vector resolved into perpendicular parts: $A_x = A\cos\theta$, $A_y = A\sin\theta$.

Add component by component, or place them head-to-tail; the resultant is the closing side.

All objects fall with the same acceleration $g$ regardless of mass (ignoring air resistance).

An object at rest has zero velocity but can still have acceleration (e.g. at the top of a toss).

A push or pull, measured in newtons (N); a vector that can change an object's motion.

Inertia: an object stays at rest or moves at constant velocity unless acted on by a net external force.

Net force equals mass times acceleration: $F_{net} = ma$.

For every force, there is an equal and opposite reaction force acting on a different object.

An object's resistance to changes in its motion, measured by its mass.

The vector sum of all forces on an object; it determines the acceleration.

A state of zero net force, so the object has zero acceleration (at rest or constant velocity).

A diagram showing one object and every force acting on it as a labeled arrow.

The gravitational force on an object's mass: $W = mg$, measured in newtons.

Mass is the amount of matter (kg), constant everywhere; weight is the force of gravity (N), which varies.

The support force a surface exerts perpendicular to itself on an object.

A force opposing relative motion between surfaces in contact.

Friction on sliding surfaces: $f_k = \mu_k N$, opposing the motion.

Friction that resists the start of sliding, up to a maximum $f_s \le \mu_s N$.

$\mu$: the ratio of the friction force to the normal force; depends on the surfaces.

The pulling force transmitted along a rope, string, or cable.

An external push or pull a person or object exerts directly.

Two forces equal in magnitude, opposite in direction, same type, acting on two different objects.

Resolve weight into components parallel ($mg\sin\theta$) and perpendicular ($mg\cos\theta$) to the surface.

The normal force you feel; it exceeds $mg$ when accelerating upward and is less when accelerating downward.

Inward acceleration in circular motion: $a_c = \dfrac{v^2}{r}$.

The net inward force keeping an object in a circle: $F_c = \dfrac{mv^2}{r}$.

Always toward the center of the circular path.

An apparent outward 'force' — actually just inertia; not a real force in an inertial frame.

Motion in a circle at constant speed, with constant-magnitude inward acceleration.

$F = \dfrac{Gm_1 m_2}{r^2}$: every mass attracts every other mass.

$g = \dfrac{F}{m}$: force per unit mass; near Earth's surface $g \approx 9.8\ \text{N/kg}$.

An orbit is free fall where gravity supplies the centripetal force keeping the object circling.

$\sum F = 0$ in every direction; the object is not accelerating.

Always in the direction of the net force (Newton's second law).

The newton (N), where $1\ \text{N} = 1\ \text{kg}\cdot\text{m/s}^2$.

Choosing what to analyze: forces internal to a system cancel; only external forces change its motion.

The single force that would put a system in equilibrium — equal and opposite to the net force.

Treat both masses as one system: $a = \dfrac{(m_1 - m_2)g}{m_1 + m_2}$.

A tilted road where the normal force's horizontal component helps supply centripetal force.

The constant speed reached when drag force balances weight, so net force and acceleration are zero.

Energy transferred by a force through a displacement: $W = Fd\cos\theta$.

Zero — a force at right angles to the motion does no work.

The SI unit of energy and work: $1\ \text{J} = 1\ \text{N}\cdot\text{m}$.

The energy of motion: $KE = \tfrac{1}{2}mv^2$.

Net work equals the change in kinetic energy: $W_{net} = \Delta KE$.

Doubling the speed quadruples the kinetic energy ($KE \propto v^2$).

Stored energy of position or configuration.

$PE_g = mgh$, relative to a chosen reference height.

$PE_s = \tfrac{1}{2}kx^2$, where $x$ is the stretch or compression.

The spring force is proportional to displacement: $F = -kx$.

$k$: the stiffness of a spring, in N/m; larger $k$ means a stiffer spring.

The sum of kinetic and potential energy: $E = KE + PE$.

When only conservative forces act, $KE + PE$ stays constant.

A force (like gravity or a spring) whose work is path-independent and stores recoverable energy.

A force (like friction) that removes mechanical energy, converting it to heat.

Total energy is never created or destroyed, only converted between forms.

Mechanical energy converted to thermal energy: $W_{friction} = f\,d$.

The rate of doing work or transferring energy: $P = \dfrac{W}{t}$.

$P = Fv$ when force is along the velocity.

The SI unit of power: $1\ \text{W} = 1\ \text{J/s}$.

Gravitational PE converts entirely to KE: $mgh = \tfrac{1}{2}mv^2$, so $v = \sqrt{2gh}$.

A diagram tracking how KE and PE trade off while their sum stays constant.

$W = mgh$ (positive when falling, negative when rising); path-independent.

Positive net work speeds an object up; negative net work slows it down.

Energy has magnitude but no direction; it is added algebraically, not as a vector.

An arbitrary chosen height where gravitational PE is defined as zero; only changes in PE matter.

Work done by a force opposing the motion (like friction), removing kinetic energy.

Useful energy output divided by total energy input; always less than 100% due to losses.

Use energy when you care about speeds and distances, not times.

For the same work, more power means the work is done in less time.

The product of mass and velocity: $p = mv$. A vector.

$\text{kg}\cdot\text{m/s}$.

The product of force and the time it acts: $J = F\Delta t$.

Impulse equals the change in momentum: $F\Delta t = \Delta p$.

On a force-time graph, the impulse equals the area under the curve.

They increase the collision time $\Delta t$, lowering the force for the same $\Delta p$.

With no net external force, total momentum before equals total momentum after.

Total momentum is conserved in every collision (when external forces are negligible).

Both momentum and total kinetic energy are conserved; objects bounce apart.

Momentum is conserved but kinetic energy is not — some becomes heat, sound, or deformation.

Objects stick together and move as one; maximum kinetic energy is lost.

Reverse of a perfectly inelastic collision: total momentum stays zero if it began at rest.

$m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2'$.

When two objects push apart, equal and opposite momenta keep total momentum constant.

Direction matters: opposite velocities subtract when finding total momentum.

The average position of a system's mass; it moves as if all mass and external force acted there.

Internal forces cancel in pairs; only external forces change total momentum.

Impulse changes momentum; work changes kinetic energy — different theorems for different questions.

$F = \dfrac{\Delta p}{\Delta t}$ — the average force during a collision.

Requires an impulse equal and opposite to its momentum.

Kinetic energy decreases; compute the loss as $KE_{before} - KE_{after}$.

Newton's second law in its general form is $F = \dfrac{\Delta p}{\Delta t}$.

Two equal masses exchange velocities in a one-dimensional elastic collision.

A system with no external forces, so its total momentum is conserved.

Impulse is a vector in the direction of the average force and the momentum change.

A projectile embeds in a block: momentum conserved in the collision, energy conserved in the swing.

Equals the impulse delivered, which equals the change in momentum.

The gun's backward momentum equals the bullet's forward momentum (total stays zero).

The angle through which an object rotates, measured in radians (symbol $\theta$).

The rate of rotation, in rad/s (symbol $\omega$).

The rate of change of angular velocity, in rad/s² (symbol $\alpha$).

$v = r\omega$: a point's linear speed equals radius times angular velocity.

The angular equations mirror the linear ones, e.g. $\omega = \omega_0 + \alpha t$.

The rotational effect of a force: $\tau = rF\sin\theta$.

The perpendicular distance from the axis to the line of the force; a longer lever arm gives more torque.

Apply force far from the axis and perpendicular to the lever arm ($\sin 90^\circ = 1$).

The newton-meter ($\text{N}\cdot\text{m}$).

Zero net torque, so no angular acceleration (the basis of balanced-beam problems).

Both net force and net torque are zero; the object neither translates nor rotates.

Resistance to changes in rotation — the rotational analog of mass (symbol $I$).

Both the total mass and how that mass is distributed about the axis.

Increases the moment of inertia, making the object harder to spin up.

$\tau_{net} = I\alpha$: net torque equals moment of inertia times angular acceleration.

Moment of inertia $I$ plays the role that mass $m$ plays in $F = ma$.

For equal mass, a hoop (mass on the rim) has a larger $I$ than a solid disk.

The line about which an object turns; torque and moment of inertia are defined relative to it.

Counterclockwise torque is conventionally positive, clockwise negative.

On a seesaw, $r_1 F_1 = r_2 F_2$ when balanced about the pivot.

The natural angle unit: $2\pi$ radians = one full revolution = $360^\circ$.

$a_t = r\alpha$: the linear acceleration of a point due to angular acceleration.

$I = mr^2$ for a single mass at distance $r$ from the axis.

A pair of equal, opposite, non-collinear forces producing pure rotation (net force zero, net torque nonzero).

$KE_{rot} = \tfrac{1}{2}I\omega^2$ — the rotational twin of $\tfrac{1}{2}mv^2$.

Translational plus rotational: $\tfrac{1}{2}mv^2 + \tfrac{1}{2}I\omega^2$.

The contact point doesn't slide, so $v = r\omega$.

Gravitational PE splits between translational and rotational KE, so it's slower than sliding.

The one with the smallest $I$ relative to its mass (a solid sphere beats a hoop).

The rotational analog of momentum: $L = I\omega$.

$\text{kg}\cdot\text{m}^2/\text{s}$.

With no external torque, $L = I\omega$ stays constant.

Pulling arms in lowers $I$, so $\omega$ rises to conserve $L$.

Pulling the arms in does work, so rotational KE increases even though $L$ is unchanged.

Net external torque equals the rate of change of angular momentum: $\tau = \dfrac{\Delta L}{\Delta t}$.

It has a direction along the axis of rotation (right-hand rule).

Its angular momentum resists changes in the axis's direction.

Linear $p = mv$ is conserved without external force; angular $L = I\omega$ without external torque.

$W = \tau\theta$: work done by a torque through an angle.

$P = \tau\omega$: the rate of rotational work.

For rolling, set $mgh = \tfrac{1}{2}mv^2 + \tfrac{1}{2}I\omega^2$ with $v = r\omega$.

Angular momentum is conserved when two rotating objects interact with no external torque.

Pulling arms in conserves angular momentum, increasing spin rate.

Its angular momentum stabilizes the direction of its spin axis (gyroscopic effect).

Oscillation where the restoring force is proportional to displacement: $F = -kx$.

A force directed back toward equilibrium that drives an oscillation.

The maximum displacement from equilibrium in an oscillation.

The time for one complete oscillation (symbol $T$).

The number of cycles per second: $f = \dfrac{1}{T}$, in hertz (Hz).

$T = 2\pi\sqrt{\dfrac{m}{k}}$ — depends only on mass and stiffness.

$T = 2\pi\sqrt{\dfrac{L}{g}}$ — depends only on length and gravity.

In SHM the period does not depend on the amplitude.

Greatest at the equilibrium position, zero at the turning points.

Greatest at maximum displacement, zero at equilibrium.

All kinetic — the spring is at natural length, so elastic PE is zero.

All potential — the object is momentarily at rest, so kinetic energy is zero.

Only small-angle swings behave as simple harmonic motion.

$\omega = 2\pi f = \dfrac{2\pi}{T}$: the rate of phase change in SHM.

An oscillation whose amplitude decreases over time due to friction or drag.

Mass per unit volume: $\rho = \dfrac{m}{V}$.

$\text{kg/m}^3$ (or g/cm³); water is $1000\ \text{kg/m}^3$.

Force per unit area: $P = \dfrac{F}{A}$.

The SI unit of pressure: $1\ \text{Pa} = 1\ \text{N/m}^2$.

Gauge pressure in a static fluid: $P = \rho g h$.

Not on container shape or total volume — only on depth and fluid density.

The upward force on an object in a fluid: $F_b = \rho V g$.

The buoyant force equals the weight of the fluid displaced.

An object floats when it is less dense than the fluid (or buoyant force ≥ weight).

An object sinks when it is denser than the fluid.

Displaces a weight of fluid exactly equal to its own weight.

For incompressible steady flow, $A_1 v_1 = A_2 v_2$ — volume flow rate is constant.

A smaller cross-section forces the fluid to move faster (continuity).

Faster-moving fluid has lower pressure (in steady, incompressible flow).

Pascal's principle: a small input force on a small piston yields a large output force on a large piston.

Pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid.

$F = PA$: pressure times area gives the force a fluid exerts on a surface.