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AP Physics 1 review: key concepts

AP Physics 1 review cards: kinematics, Newton's laws, energy, momentum, torque and rotation, oscillations and fluids, each with a numbered worked example.

43 cards6 topicsAbout 15 minutes a roundAP Physics 1 style course content (algebra-based first-term mechanics, including rotation, oscillations and fluids)

Independent study material written by StudyBrix. AP and SAT are trademarks of College Board and ACT is a trademark of ACT, Inc.; neither organisation is involved with or has reviewed this deck.

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About this deck

This deck supports students in an algebra-based AP Physics 1 style course, and anyone reviewing first-term mechanics without calculus. It covers kinematics and graphs, forces and Newton's laws, circular motion and gravitation, work, energy and power, linear momentum and collisions, torque and rotational dynamics, rotational energy and angular momentum, simple harmonic motion, and fluids (pressure, buoyancy and flow).

You need solid algebra, right triangle trigonometry (sine, cosine and tangent to split vectors into components) and a working sense of units. All examples use g = 9.8 m/s^2; some courses round to 10 m/s^2, which changes answers slightly. Solve each example yourself before flipping, and always write the starting equation before substituting numbers.

Physics exams reward reasoning as much as arithmetic. For every card, try a second version of the question in words: what happens to the answer if the mass doubles, or the radius halves? Sketch a free-body diagram for every force problem and an energy bar chart for energy problems; those representations often earn credit on their own.

Common mistakes: drawing the normal force as always equal to mg (it is not on an incline or in an accelerating elevator); treating the two forces of a Newton's third law pair as if they act on the same object; and assuming kinetic energy is conserved in every collision. Momentum is conserved whenever external impulses are negligible, but kinetic energy is conserved only in elastic collisions.

Before you start: Grade 11 or 12 algebra and right triangle trigonometry; an introductory physics course helps but is not required.

All 43 cards

Cover the definitions with a sheet of paper and test yourself, or use the study modes above.

Kinematics

Displacement versus distance: Displacement is the change in position, a vector with direction; distance is the total path length, a scalar that is never negative.Example: Walk 3 m east then 3 m west: distance 6 m, displacement 0 m.
Average velocity: Displacement divided by elapsed time; its direction matches the displacement.Example: Moving from x = 2 m to x = 14 m in 4 s gives (14 - 2)/4 = 3 m/s.
v = v0 + a t: Constant acceleration relation linking final velocity, initial velocity, acceleration and time.Example: A car starts from rest at 3 m/s^2 for 4 s: v = 12 m/s, and it travels (1/2)(3)(4^2) = 24 m.
v^2 = v0^2 + 2 a delta x: Constant acceleration relation that does not involve time; useful for stopping distances.Example: Braking from 20 m/s at -5 m/s^2: 0 = 400 - 10 delta x, so delta x = 40 m.
Free fall: Motion under gravity alone, with acceleration 9.8 m/s^2 downward regardless of mass (air resistance ignored).Example: Dropped from rest for 2.0 s: speed 19.6 m/s and drop (1/2)(9.8)(2.0^2) = 19.6 m.
Horizontally launched projectile: Horizontal velocity stays constant while vertical motion is free fall; the two are linked only by time.Example: From 4.9 m high, fall time is 1.0 s; launched at 3 m/s it lands 3 m away.
Slopes and areas of motion graphs: Slope of position vs time is velocity; slope of velocity vs time is acceleration; area under velocity vs time is displacement.Example: Constant 4 m/s for 5 s: the area under the velocity graph is 20 m.

Forces and Newton's laws

Newton's first law: An object keeps its velocity (including staying at rest) unless a nonzero net external force acts; this tendency is inertia.Example: A puck on nearly frictionless ice keeps sliding in a straight line.
Newton's second law: Net force equals mass times acceleration, F net = m a, with acceleration in the direction of the net force.Example: A 10 N net force on a 2.0 kg cart gives a = 5.0 m/s^2.
Newton's third law: When object A pushes on object B, B pushes on A with an equal and opposite force; the pair acts on different objects and is the same type of force.Example: Your foot pushes back on the ground and the ground pushes you forward.
Free-body diagram: A sketch of one object showing every external force on it as an arrow from the object, labelled by type and source.Example: A book resting on a table: weight down and normal force up, equal in size.
Normal force in an accelerating elevator: The contact force from a surface; it equals m(g + a) when the floor accelerates upward and m(g - a) when it accelerates downward.Example: 60 kg person, elevator accelerating up at 2.0 m/s^2: N = 60(9.8 + 2.0) = 708 N.
Kinetic friction: Force opposing sliding once surfaces are moving, f = mu_k N, where mu_k is the sliding coefficient for the two surfaces.Example: 5.0 kg box on a level floor with mu_k = 0.20: f = 0.20 x 5.0 x 9.8 = 9.8 N.
Static friction: Force that prevents surfaces from starting to slide; it adjusts up to a maximum of mu_s N.Example: If mu_s = 0.5 and N = 40 N, a 15 N push is matched exactly and the crate stays put.
Object on an incline: Split gravity into mg sin(theta) along the slope and mg cos(theta) into the slope; the normal force balances the second part when there is no other perpendicular force.Example: Frictionless 30 degree ramp: a = 9.8 sin 30 = 4.9 m/s^2.
Atwood machine: Two connected masses share one acceleration; treat them as a system so tension cancels internally.Example: 3.0 kg and 2.0 kg hung over a pulley: a = (3.0 - 2.0)(9.8)/5.0 = 1.96 m/s^2.
Hooke's law: An ideal spring exerts a restoring force proportional to stretch or compression: F = -k x.Example: k = 200 N/m stretched 0.050 m pulls back with 10 N.
Centripetal acceleration: An object moving in a circle at constant speed accelerates toward the centre with a = v^2/r; some real force must supply m v^2/r.Example: 10 m/s around a 20 m radius curve: a = 100/20 = 5.0 m/s^2.
Newton's law of universal gravitation: Every pair of masses attracts with F = G m1 m2/r^2, so the force falls with the square of the distance between centres.Example: Doubling the distance between two moons cuts the force to one quarter.

Energy and power

Work done by a constant force: W = F d cos(theta), where theta is the angle between force and displacement; measured in joules.Example: Pulling with 50 N at 60 degrees over 4.0 m: W = 50 x 4.0 x 0.5 = 100 J.
Kinetic energy: Energy of motion, K = (1/2) m v^2.Example: A 2.0 kg ball at 3.0 m/s has (1/2)(2.0)(9.0) = 9.0 J.
Gravitational potential energy near Earth: U = m g h measured from a chosen reference height; only changes in U matter.Example: Lifting 3.0 kg by 2.0 m stores 3.0 x 9.8 x 2.0 = 58.8 J.
Elastic potential energy: Energy stored in a stretched or compressed spring, U = (1/2) k x^2.Example: k = 200 N/m compressed 0.10 m: U = (1/2)(200)(0.01) = 1.0 J.
Conservation of mechanical energy: With no friction or other nonconservative work, K + U stays constant for a system.Example: Dropped from 5.0 m: v = sqrt(2 x 9.8 x 5.0) = 9.9 m/s at the ground.
Work-energy theorem: The net work done on an object equals its change in kinetic energy.Example: Net work of 36 J on a 2.0 kg cart from rest gives v = sqrt(36) = 6.0 m/s.
Power: Rate of energy transfer, P = W/t or P = F v; measured in watts.Example: Lifting a load with 600 J of work in 3.0 s takes 200 W.

Momentum

Linear momentum: Mass times velocity, p = m v, a vector measured in kg m/s.Example: A 1200 kg car at 15 m/s has 18 000 kg m/s.
Impulse: Force times the time it acts, J = F delta t, which equals the change in momentum.Example: 0.15 kg ball at 40 m/s returned at 30 m/s: J = 0.15 x 70 = 10.5 N s; over 0.010 s, F = 1050 N.
Perfectly inelastic collision: Objects stick together after impact; momentum is conserved but kinetic energy decreases the most.Example: 2.0 kg at 3.0 m/s hits 1.0 kg at rest and sticks: v = 6.0/3.0 = 2.0 m/s; KE goes from 9.0 J to 6.0 J.
Elastic collision: A collision in which both momentum and total kinetic energy are conserved.Example: Equal masses, one at rest: in a head-on elastic hit they exchange velocities.
Velocity of the centre of mass: With no net external force, the centre of mass of a system keeps a constant velocity, even during internal explosions or collisions.Example: A firework shell bursting in mid-air: the pieces' centre of mass keeps following the original path.

Rotation

Torque: The turning effect of a force about an axis, tau = r F sin(theta), where r is the distance from the axis to where the force acts.Example: 20 N applied perpendicular at 0.50 m from a hinge gives 10 N m.
Rotational equilibrium: Net torque about any axis is zero (and net force is zero), so clockwise and counterclockwise torques balance.Example: Seesaw: 30 kg at 2.0 m balances 40 kg at 1.5 m, since 30 x 2.0 = 40 x 1.5 = 60.
Rotational inertia: Resistance to angular acceleration; depends on mass and how far it sits from the axis. A point mass has m r^2; a solid disc has (1/2) M R^2.Example: A 2.0 kg disc of radius 0.30 m: I = 0.5 x 2.0 x 0.09 = 0.090 kg m^2.
Rotational form of Newton's second law: Net torque equals rotational inertia times angular acceleration, tau net = I alpha.Example: A 0.90 N m torque on I = 0.090 kg m^2 gives alpha = 10 rad/s^2.
Conservation of angular momentum: With no net external torque, L = I omega stays constant, so reducing I increases omega.Example: A skater halves her rotational inertia by pulling in her arms and spins twice as fast.
Rotational kinetic energy: Energy of spinning, K = (1/2) I omega^2; a rolling object has this energy plus translational K = (1/2) m v^2.Example: I = 0.090 kg m^2 spinning at 10 rad/s stores 0.5 x 0.090 x 100 = 4.5 J.

Oscillations and fluids

Period of a mass on a spring: T = 2 pi sqrt(m/k); it does not depend on amplitude.Example: m = 0.50 kg and k = 50 N/m: T = 2 pi sqrt(0.010) = 0.63 s.
Period of a simple pendulum: For small swings T = 2 pi sqrt(L/g), independent of the bob's mass.Example: L = 1.0 m: T = 2 pi sqrt(1.0/9.8) = 2.0 s.
Pressure at depth in a fluid: P = P0 + rho g h: pressure rises with depth in proportion to fluid density.Example: 10 m down in fresh water adds 1000 x 9.8 x 10 = 98 000 Pa to the surface pressure.
Buoyant force (Archimedes' principle): An upward force equal to the weight of fluid displaced: F = rho(fluid) V(displaced) g.Example: A 0.0020 m^3 block fully under water feels 1000 x 0.0020 x 9.8 = 19.6 N upward.
Continuity equation: For an incompressible fluid, A1 v1 = A2 v2: flow speeds up where the pipe narrows.Example: If the cross-section halves, the speed doubles.
Bernoulli's equation: Along a streamline, P + (1/2) rho v^2 + rho g y is constant, so where fluid moves faster at the same height, pressure is lower.Example: Air moving faster over the top of a curved wing lowers pressure there, contributing to lift.