## A Space, time and motion

### A.1 Kinematics

- The students should understand that the motion of bodies through space and time can be described and analysed in terms of position, velocity, and acceleration (SL and HL)
- The students should understand that the motion of bodies through space and time can be described and analysed in terms of position, velocity, and acceleration (SL and HL)
- The students should understand velocity is the rate of change of position, and acceleration is the rate of change of velocity (SL and HL)
- The students should understand the change in position is the displacement (SL and HL)
- The students should understand the change in position is the displacement (SL and HL)
- The students should understand the difference between instantaneous and average values of velocity, speed and acceleration, and how to determine them (SL and HL)
- The students should understand the equations of motion for solving problems with uniformly accelerated motion as given by, s=(u+t/2)t, v=u+at, s=ut+(1/2)at^2, v^2=u^2+2as (SL and HL)
- The students should understand motion with uniform and non-uniform acceleration (SL and HL)
- The students should understand the behaviour of projectiles in the absence of fluid resistance, and the application of the equations of motion resolved into vertical and horizontal components (SL and HL)
- The students should understand the qualitative effect of fluid resistance on projectiles, including time of flight, trajectory, velocity, acceleration, range and terminal speed. (SL and HL)

### A.2 Forces and momentum

- The students should understand Newton’s three laws of motion (SL and HL)
- The students should understand that forces acting on a body can be represented in a free-body diagram (SL and HL)
- The students should understand that free-body diagrams can be analysed to find the resultant force on a system (SL and HL)
- The students should understand the nature and use of the following contact forces: surface frictional force Ff acting in a direction parallel to the plane of contact between a body and a surface, on a stationary body as given by Ff ≤ μsFN or a body in motion as given by Ff = μdFN where μs and μd are the coefficients of static and dynamic friction respectively (SL and HL)
- The students should understand the nature and use of the following contact forces: elastic restoring force FH following Hooke’s law as given by FH = –kx where k is the spring constant (SL and HL)
- The students should understand the nature and use of the following field forces: electric force Fe (SL and HL)
- The students should understand that linear momentum as given by p = mv remains constant unless the system is acted upon by a resultant external force (SL and HL)
- The students should understand that a resultant external force applied to a system constitutes an impulse J as given by J = FΔt where F is the average resultant force and Δt is the time of contact (SL and HL)
- The students should understand the elastic and inelastic collisions of two bodies (SL and HL)
- The students should understand explosions (SL and HL)
- The students should understand energy considerations in elastic collisions, inelastic collisions, and explosions (SL and HL)
- The students should understand that bodies moving along a circular trajectory at a constant speed experience an acceleration that is directed radially towards the centre of the circle—known as a centripetal acceleration as given by a = v2/r = w2r=4π2r/T2 (SL and HL)
- The students should understand that circular motion is caused by a centripetal force acting perpendicular to the velocity (SL and HL)
- The students should understand that a centripetal force causes the body to change direction even if its magnitude of velocity may remain constant (SL and HL)
- The students should understand that the motion along a circular trajectory can be described in terms of the angular velocity ω which is related to the linear speed v by the equation as given by v=2πr/T=wr (SL and HL)

### A.3 Work, energy and power

- The students should understand the principle of the conservation of energy (SL and HL)
- The students should understand that work done by a force is equivalent to a transfer of energy (SL and HL)
- The students should understand that mechanical energy is the sum of kinetic energy, gravitational potential energy and elastic potential energy (SL and HL)
- The students should understand that if mechanical energy is conserved, work is the amount of energy transformed between different forms of mechanical energy in a system, such as: the kinetic energy of translational motion as given by Ek = 1/2mv2 = p2/2m (SL and HL)
- The students should understand that if mechanical energy is conserved, work is the amount of energy transformed between different forms of mechanical energy in a system, such as: the gravitational potential energy, when close to the surface of the Earth as given by ΔEp = mgΔh (SL and HL)
- that if mechanical energy is conserved, work is the amount of energy transformed between different forms of mechanical energy in a system, such as: the elastic potential energy as given by EH = 1/2k(Δx)2 (SL and HL)
- The students should understand that power developed P is the rate of work done, or the rate of energy transfer, as given by P = ΔW/Δt = Fv (SL and HL)

### A.4 Rigid body mechanics

- The students should understand the torque τ of a force about an axis as given by τ = Fr sin θ (SL and HL)
- The students should understand that bodies in rotational equilibrium have a resultant torque of zero (AHL)
- The students should understand that an unbalanced torque applied to an extended, rigid body will cause angular acceleration (AHL)
- The students should understand that the rotation of a body can be described in terms of angular displacement, angular velocity and angular acceleration (AHL)
- The students should understand that the moment of inertia I depends on the distribution of mass of an extended body about an axis of rotation (AHL)
- The students should understand the moment of inertia for a system of point masses as given by I = Σmr2 (AHL)
- The students should understand Newton’s second law for rotation as given by τ = Iα where τ is the average torque (AHL)
- The students should understand that an extended body rotating with an angular speed has an angular momentum L as given by L = Iω (AHL)
- The students should understand that angular momentum remains constant unless the body is acted upon by a resultant torque (AHL)
- The students should understand that the action of a resultant torque constitutes an angular impulse ΔL as given by ΔL = τΔt = Δ(Iω) (AHL)

## B The particulate nature of matter

### B.1 Thermal energy transfers

### B.3 Gas Laws

- The students should understand that ideal gases are described in terms of the kinetic theory and constitute a modelled system used to approximate the behaviour of real gases (SL and HL)
- The students should understand that the ideal gas law equation can be derived from the empirical gas laws for constant pressure, constant volume and constant temperature as given by PV/T = constant (SL and HL)

### B.4 Thermodynamics

- The students should understand that isovolumetric, isobaric, isothermal and adiabatic processes are obtained by keeping one variable fixed (AHL)
- The students should understand that cyclic gas processes are used to run heat engines (AHL)

### B.5 Currents and Circuits

- The students should understand that circuit diagrams represent the arrangement of components in a circuit (SL and HL)
- The students should understand electrical resistance R as given by R = V/I (SL and HL)
- The students should understand resistivity as given by ρ = RA/L (SL and HL)
- The students should understand Ohm’s law (SL and HL)
- The students should understand the combinations of resistors in series and parallel circuits. Series circuits: I = I1 = I2 = Ω, V = V1 + V2 + Ω, RS = R1 + R2 + Ω, Parallel circuits: I = I1 + I2 + Ω, V = V1 = V2 = Ω, 1/Rp=1/R1+1/R2+Ω (SL and HL)

## C Wave behaviour

### C.1 Simple harmonic motion

- The students should understand a particle undergoing simple harmonic motion can be described using time period T, frequency ƒ, angular frequency ω, amplitude, equilibrium position, and displacement (SL and HL)
- The students should understand the time period in terms of frequency of oscillation and angular frequency as given by T = 1/ƒ = 2π/ω (SL and HL)
- The students should understand the time period of a mass–spring system as given by T = 2π √m/k (SL and HL)
- The students should understand the time period of a simple pendulum as given by T = 2π√l/g (SL and HL)
- The students should understand a qualitative approach to energy changes during one cycle of an oscillation. (SL and HL)

### C.2 Wave model

### C.3 Wave phenomena

- The students should understand the condition for constructive interference as given by path difference = nλ (SL and HL)
- The students should understand the condition for destructive interference as given by path difference = (n +1/2)λ (SL and HL)
- The students should understand Young’s double-slit interference as given by s = λD/d where s is the separation of fringes, d is the separation of the slits, and D is the distance from the slits to the screen (SL and HL)
- The students should understand single-slit diffraction including intensity patterns as given by θ = λ/b where b is the slit width (AHL)
- The students should understand that the single-slit pattern modulates the double slit interference pattern (AHL)
- The students should understand interference patterns from multiple slits and diffraction gratings as given by nλ = d sin θ (AHL)

### C.4 Standing waves and resonance

- The students should understand the nature and formation of standing waves in terms of superposition of two identical waves travelling in opposite directions (SL and HL)
- The students should understand nodes and antinodes, relative amplitude and phase difference of points along a standing wave (SL and HL)
- The students should understand standing waves patterns in strings and pipes (SL and HL)
- The students should understand the nature of resonance including natural frequency and amplitude of oscillation based on driving frequency (SL and HL)

### C.5 Doppler effect

- The students should understand the nature of the Doppler effect for sound waves and electromagnetic waves (SL and HL)
- The students should understand the representation of the Doppler effect in terms of wavefront diagrams when either the source or the observer is moving (SL and HL)
- The students should understand the observed frequency for sound waves and mechanical waves due to the Doppler effect as given by: moving source ƒ′ = ƒ (v/v±us) where us is the velocity of the source, moving observer ƒ′ = ƒ(v±uo/v) v where uo is the velocity of the observer. (AHL)

## D Fields

### D.2 Electrical magnetic fields

- The students should understand Coulomb’s law as given by F = k(q1q2/r2) for charged bodies treated as point charges where k = 1/4πε0 (SL and HL)
- The students should understand the electric field strength as given by E = F/q (SL and HL)
- The students should understand electric field lines (SL and HL)
- The students should understand the relationship between field line density and field strength (SL and HL)
- The students should understand the uniform electric field strength between parallel plates as given by E = V/d (SL and HL)
- The students should understand the electric field strength E as the electric potential gradient as given by E = –ΔVe/Δr (AHL)
- The students should understand the work done in moving a charge q in an electric field as given by W = qΔVe (AHL)
- The students should understand equipotential surfaces for electric fields (AHL)
- The students should understand the relationship between equipotential surfaces and electric field lines (AHL)

### D.4 Induction

## E Nuclear and quantum physics

### E.1 Structure of the atom

- The students should understand hat emission and absorption spectra provide evidence for discrete atomic energy levels (SL and HL)
- The students should understand that photons are emitted and absorbed during atomic transitions (SL and HL)
- The students should understand that the frequency of the photon released during an atomic transition depends on the difference in energy level as given by E = hƒ (SL and HL)
- The students should understand that emission and absorption spectra provide information on the chemical composition. (SL and HL)
- The students should understand the discrete energy levels in the Bohr model for hydrogen as given by E = − (13.6/n2) eV (AHL)

### E.2 Quantum physics

- The students should understand the photoelectric effect as evidence of the particle nature of light (AHL)
- The students should understand that photons of a certain frequency, known as the threshold frequency, are required to release photoelectrons from the metal (AHL)
- The students should understand Einstein’s explanation using the work function and the maximum kinetic energy of the photoelectrons as given by Emax = hƒ–Φ where Φ is the work function of the metal (AHL)

### E.3 Radioactive decay

- The students should understand the random and spontaneous nature of radioactive decay (SL and HL)
- The students should understand the radioactive decay equations involving α, β−, β+, γ (SL and HL)
- The students should understand the penetration and ionizing ability of alpha particles, beta particles and gamma rays (SL and HL)
- The students should understand the activity, count rate and half-life in radioactive decay (SL and HL)
- The students should understand the changes in activity and count rate during radioactive decay using integer values of half-life (SL and HL)
- The students should understand the effect of background radiation on count rate. (SL and HL)