First-year courses · Sciences

Physics I: mechanics

Kinematics, Newton's laws, friction, work and energy, momentum, rotation, oscillations and gravitation, with SI units and worked numbers in each card.

45 cards6 topicsAbout 20 minutes a roundTypical first-year calculus-based or algebra-based physics, mechanics term

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About this deck

This deck follows a first-term university mechanics course: motion in one and two dimensions, Newton's laws and free-body diagrams, friction and circular motion, work, kinetic and potential energy, power, momentum and collisions, rotational motion with torque and moment of inertia, simple harmonic motion and universal gravitation. Every quantity is given in SI units, and examples use g = 9.8 m/s^2 unless stated otherwise.

You should be comfortable with algebra, trigonometry (resolving a vector into components with sine and cosine) and basic vector ideas. Many courses also use derivatives for velocity and acceleration; the cards mention them but do not depend on heavy calculus.

Physics flashcards work best when you treat each example as a mini problem: cover it, set it up yourself, and check that your units come out right before looking. For the formula cards, say aloud what each symbol means and under what conditions the formula holds (constant acceleration, small angles, isolated system). Mix tags often, because exam problems combine ideas, such as energy conservation to find a speed and then momentum for a collision.

Common mistakes: using the constant-acceleration equations when acceleration is not constant; setting the normal force equal to mg on an incline or in an accelerating elevator; and assuming kinetic energy is conserved in every collision (only momentum is guaranteed, and only for an isolated system). Watch signs too: choose a positive direction at the start and stick to it.

Before you start: Grade 12 physics is helpful but not required; Grade 12 algebra and trigonometry are needed, and first-year calculus alongside is common.

All 45 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, can be negative); distance is the total length of path travelled (a scalar, never negative).Example: Walk 5 m east then 3 m west: displacement 2 m east, distance 8 m.
Average velocity: Displacement divided by the time interval: delta x/delta t, in m/s.Example: A runner moves 120 m along a straight track in 8 s: average velocity 15 m/s.
Instantaneous velocity: The rate of change of position at one moment, v = dx/dt; the slope of the position-time graph.Example: x(t) = 4t^2 m gives v = 8t, so v = 16 m/s at t = 2 s.
Acceleration: The rate of change of velocity, a = dv/dt, measured in m/s^2. It can change speed, direction, or both.Example: A car going from 0 to 27 m/s in 9 s has average acceleration 3 m/s^2.
Constant-acceleration equations: With constant a: v = v0 + at; x = x0 + v0 t + (1/2)at^2; v^2 = v0^2 + 2a(x - x0).Example: From rest at 3 m/s^2 for 4 s: v = 12 m/s and displacement = 0.5(3)(16) = 24 m.
Free fall: Motion under gravity alone, with downward acceleration of magnitude g = 9.8 m/s^2 near Earth's surface (air resistance ignored).Example: Dropped from 20 m: t = sqrt(2(20)/9.8) = 2.02 s.
Projectile motion: Horizontal velocity stays constant while vertical motion has acceleration g downward; the two are solved separately and linked by time.Example: 20 m/s at 30 degrees on level ground: range = v^2 sin(2 theta)/g = 400(0.866)/9.8 = 35.3 m.
Relative velocity: The velocity of A as measured by B: v(A rel B) = v(A rel ground) - v(B rel ground).Example: Train at 30 m/s, you walk forward at 1.5 m/s inside: 31.5 m/s relative to the ground.

Forces and Newton's laws

Newton's first law: An object keeps a constant velocity (including staying at rest) unless a nonzero net force acts on it; also called the law of inertia.Example: A puck on frictionless ice slides at constant speed after it is struck.
Newton's second law: The net force on an object equals its mass times its acceleration: F_net = ma, with force in newtons (1 N = 1 kg m/s^2).Example: A 5 N net force on a 2 kg cart gives a = 2.5 m/s^2.
Newton's third law: When A pushes on B, B pushes back on A with a force equal in size and opposite in direction; the two forces act on different objects.Example: Your feet push back on the ground and the ground pushes you forward when you walk.
Weight: The gravitational force on an object, W = mg, directed toward the centre of the Earth; it differs from mass, which is measured in kg.Example: A 70 kg person has weight 70(9.8) = 686 N.
Normal force: The contact force a surface exerts perpendicular to itself; its size is whatever is needed to stop objects passing through, not always mg.Example: 70 kg person in an elevator accelerating up at 2 m/s^2: N = 70(9.8 + 2) = 826 N.
Free-body diagram: A sketch of one object showing every external force acting on it as an arrow from the object, used to write Newton's second law in components.Example: Block on a ramp: weight (down), normal force (perpendicular to ramp), friction (along ramp).
Kinetic friction: The force opposing sliding between surfaces in contact: f_k = mu_k N, where mu_k is a dimensionless coefficient for the pair of surfaces in motion.Example: 10 kg box on a level floor with mu_k = 0.3: f_k = 0.3(98) = 29.4 N.
Static friction: The force that prevents surfaces from starting to slide; it adjusts up to a maximum of mu_s N.Example: mu_s = 0.5, N = 98 N: it can hold up to 49 N of applied push before the box moves.
Inclined plane components: On a slope at angle theta, weight splits into mg sin(theta) along the slope and mg cos(theta) perpendicular to it.Example: Frictionless 30 degree ramp: a = g sin 30 = 4.9 m/s^2 down the slope.
Centripetal acceleration: In uniform circular motion, acceleration points to the centre with size v^2/r; the net inward force needed is mv^2/r.Example: 10 m/s on a curve of radius 50 m: a = 100/50 = 2 m/s^2.
Tension: The pulling force transmitted along a rope or cable; for an ideal massless rope it is the same throughout.Example: A 2 kg mass hanging at rest from a rope: T = 2(9.8) = 19.6 N.

Work and energy

Work done by a constant force: W = F d cos(theta), where theta is the angle between force and displacement; measured in joules (1 J = 1 N m).Example: 10 N at 60 degrees to a 5 m displacement: W = 10(5)(0.5) = 25 J.
Kinetic energy: Energy of motion, K = (1/2)mv^2, in joules.Example: A 2 kg ball at 3 m/s has K = 0.5(2)(9) = 9 J.
Work-energy theorem: The net work done on an object equals its change in kinetic energy: W_net = K_final - K_initial.Example: Net work of 16 J on a 2 kg ball at rest: v = sqrt(2(16)/2) = 4 m/s.
Gravitational potential energy (near Earth): U = mgh relative to a chosen reference level; only changes in U have physical meaning.Example: Lifting 2 kg by 5 m raises U by 2(9.8)(5) = 98 J.
Hooke's law and spring energy: An ideal spring exerts F = -kx (k in N/m) and stores elastic potential energy (1/2)kx^2.Example: k = 200 N/m stretched 0.1 m: force 20 N, stored energy 0.5(200)(0.01) = 1 J.
Conservation of mechanical energy: When only conservative forces do work, K + U stays constant.Example: Drop from 20 m: mgh = (1/2)mv^2 gives v = sqrt(2(9.8)(20)) = 19.8 m/s.
Power: The rate of doing work, P = W/t (also P = Fv), measured in watts (1 W = 1 J/s).Example: Lifting 50 kg by 2 m in 4 s: 980 J/4 s = 245 W.
Conservative force: A force whose work between two points does not depend on the path, so a potential energy can be defined for it; gravity and ideal springs qualify, friction does not.Example: Carrying a box up stairs or up a ramp to the same height: gravity does the same work either way.

Momentum and collisions

Linear momentum: p = mv, a vector in kg m/s.Example: A 1500 kg car at 20 m/s has momentum 30 000 kg m/s.
Impulse: The product of average force and time interval, J = F delta t; it equals the change in momentum.Example: 0.15 kg ball goes from 40 m/s to -30 m/s: delta p = -10.5 kg m/s; over 0.01 s the average force is 1050 N.
Conservation of momentum: If the net external force on a system is zero, the total momentum of the system stays constant, including through collisions and explosions.Example: A 60 kg skater pushes a 40 kg skater from rest; if the 40 kg one moves at 3 m/s, the 60 kg one moves at 2 m/s the other way.
Perfectly inelastic collision: Objects stick together after colliding; momentum is conserved but kinetic energy is lost (the maximum possible loss).Example: 2 kg at 3 m/s hits 1 kg at rest: v = 6/3 = 2 m/s; K drops from 9 J to 6 J.
Elastic collision: A collision in which both momentum and kinetic energy are conserved.Example: Head-on, equal masses, one at rest: the moving one stops and the other leaves with its velocity.
Centre of mass: The mass-weighted average position, x_cm = (sum of m_i x_i)/(sum of m_i); external forces accelerate it as if all mass were there.Example: 2 kg at x = 0 and 3 kg at x = 5 m: x_cm = 15/5 = 3 m.

Rotation

Angular velocity: Rate of change of angle, omega = d(theta)/dt in rad/s; a point at radius r moves with linear speed v = r omega.Example: A 0.3 m radius wheel at 10 rad/s: rim speed 3 m/s.
Torque: The turning effect of a force: tau = r F sin(theta), where r is the distance from the axis; unit N m.Example: 20 N applied perpendicular at 0.5 m from a hinge: tau = 10 N m.
Moment of inertia: Rotational inertia, I = sum of m r^2; it depends on how mass is distributed about the axis.Example: Solid disc, I = (1/2)MR^2: 2 kg, radius 0.5 m gives 0.25 kg m^2.
Newton's second law for rotation: Net torque equals moment of inertia times angular acceleration: tau_net = I alpha.Example: 10 N m on a 0.25 kg m^2 disc: alpha = 40 rad/s^2.
Rotational kinetic energy: K_rot = (1/2) I omega^2; a rolling object has both this and translational kinetic energy.Example: I = 0.25 kg m^2 at 8 rad/s: K = 0.5(0.25)(64) = 8 J.
Angular momentum: L = I omega for a rigid body; it is conserved when net external torque is zero.Example: A skater pulls in her arms, halving I, so omega doubles.
Static equilibrium: An object stays at rest when both the net force and the net torque about any axis are zero.Example: Seesaw: 30 kg child at 2 m balances a 40 kg child at 1.5 m (60 = 60).

Oscillations and gravitation

Simple harmonic motion: Oscillation where the restoring acceleration is proportional to displacement, a = -omega^2 x, giving x(t) = A cos(omega t + phi).Example: A mass on an ideal spring moves this way, with omega = sqrt(k/m).
Period of a mass-spring system: T = 2 pi sqrt(m/k); independent of amplitude.Example: 0.5 kg on a 200 N/m spring: T = 2 pi sqrt(0.0025) = 0.314 s.
Period of a simple pendulum: T = 2 pi sqrt(L/g) for small swings; independent of the bob's mass.Example: L = 1.0 m: T = 2 pi sqrt(1/9.8) = 2.01 s.
Newton's law of universal gravitation: Any two masses attract with F = G m1 m2/r^2, where G = 6.674 x 10^(-11) N m^2/kg^2 and r is the centre-to-centre distance.Example: Two 100 kg spheres 1 m apart: F = 6.67 x 10^(-7) N.
Orbital speed: For a circular orbit, gravity supplies the centripetal force, giving v = sqrt(GM/r), with r measured from the planet's centre.Example: About 400 km above Earth (r = 6.77 x 10^6 m, M = 5.97 x 10^24 kg): v is about 7.67 km/s.