conditions that lead to simple harmonic motion

Delving into the IB Physics syllabus offers a comprehensive overview of the knowledge you'll gain during the course. Join us as we break down the core concepts of the syllabus, providing you with a clearer insight into what to anticipate on your learning path.

The IB Physics Syllabus is made up of 5 themes. Each theme consists of a variety of topics.

Physics

In this theme, you will explore the following topics:

Space, time and motion

that the motion of bodies through space and time can be described and analysed in terms of position, velocity, and acceleration

velocity is the rate of change of position, and acceleration is the rate of change of velocity

the change in position is the displacement

the difference between distance and displacement

the difference between instantaneous and average values of velocity, speed and acceleration, and how to determine them

the equations of motion for solving problems with uniformly accelerated motion as given by u+v s= t 2 v = u + at 1 s = ut + at2 2 v2 = u2 + 2as

motion with uniform and non-uniform acceleration

the behaviour of projectiles in the absence of fluid resistance, and the application of the equations of motion resolved into vertical and horizontal components

the qualitative effect of fluid resistance on projectiles, including time of flight, trajectory, velocity, acceleration, range and terminal speed.

Kinematics

that forces acting on a body can be represented in a free-body diagram

that free-body diagrams can be analysed to find the resultant force on a system

the nature and use of the following contact forces ◦ normal force FN is the component of the contact force acting perpendicular to the surface that counteracts the body ◦ 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 ◦ tension ◦ elastic restoring force FH following Hooke’s law as given by FH = –kx where k is the spring constant ◦ viscous drag force Fd acting on a small sphere opposing its motion through a fluid as given by Fd = 6πηrv where η is the fluid viscosity, r is the radius of the sphere and v is the velocity of the sphere through the fluid ◦ buoyancy Fb acting on a body due to the displacement of the fluid as given by Fb = ρVg where V is the volume of fluid displaced

the nature and use of the following field forces ◦ gravitational force Fg is the weight of the body and calculated is given by Fg = mg ◦ electric force Fe ◦ magnetic force Fm

that linear momentum as given by p = mv remains constant unless the system is acted upon by a resultant external force

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

that the applied external impulse equals the change in momentum of the system

Δp that Newton’s second law in the form F = ma assumes mass is constant whereas F = allows for Δt situations where mass is changing

the elastic and inelastic collisions of two bodies

energy considerations in elastic collisions, inelastic collisions, and explosions

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 v2 4π 2r a= = ω2r = 2 r T

that circular motion is caused by a centripetal force acting perpendicular to the velocity

that a centripetal force causes the body to change direction even if its magnitude of velocity may remain constant

that the motion along a circular trajectory can be described in terms of the angular velocity ω which is 2πr related to the linear speed v by the equation as given by v = = ωr.

Forces and momentum

the principle of the conservation of energy

that work done by a force is equivalent to a transfer of energy

that energy transfers can be represented on a Sankey diagram

that work W done on a body by a constant force depends on the component of the force along the line of displacement as given by W = Fs cos θ

that work done by the resultant force on a system is equal to the change in the energy of the system

that mechanical energy is the sum of kinetic energy, gravitational potential energy and elastic potential energy

that in the absence of frictional, resistive forces, the total mechanical energy of a system is conserved

that if mechanical energy is conserved, work is the amount of energy transformed between different forms of mechanical energy in a system, such as: ◦ 1 p2 the kinetic energy of translational motion as given by Ek = mv2 = 2 2m ◦ the gravitational potential energy, when close to the surface of the Earth as given by ΔEp = mgΔh ◦ 1 the elastic potential energy as given by EH = k(Δx)2 2

that power developed P is the rate of work done, or the rate of energy transfer, as given by ΔW P= = Fv Δt

Eoutput Poutput efficiency η in terms of energy transfer or power as given by η = = Einput Pinput

Work, energy and power

the torque τ of a force about an axis as given by τ = Fr sin θ

that bodies in rotational equilibrium have a resultant torque of zero

that an unbalanced torque applied to an extended, rigid body will cause angular acceleration

that the rotation of a body can be described in terms of angular displacement, angular velocity and angular acceleration

that equations of motion for uniform angular acceleration can be used to predict the body’s angular position θ, angular displacement Δθ, angular speed ω and angular acceleration α, as given by ωf + ωi Δθ = t 2 ωf = ωi + αt 1 Δθ = ωit + αt2 2 ωf2 = ωi2 + 2αΔθ

that the moment of inertia I depends on the distribution of mass of an extended body about an axis of rotation

the moment of inertia for a system of point masses as given by I = Σmr2

Newton’s second law for rotation as given by τ = Iα where τ is the average torque

that an extended body rotating with an angular speed has an angular momentum L as given by L = Iω

that angular momentum remains constant unless the body is acted upon by a resultant torque

that the action of a resultant torque constitutes an angular impulse ΔL as given by ΔL = τΔt = Δ(Iω)

1 2 L2 the kinetic energy of rotational motion as given by Ek = Iω = .

Rigid body mechanics

that Newton's laws of motion are the same in all inertial reference frames and this is known as Galilean relativity

that in Galilean relativity the position x′ and time t′ of an event are given by x′ = x–vt and t′ = t

that Galilean transformation equations lead to the velocity addition equation as given by u′ = u–v

that the postulates of special relativity lead to the Lorentz transformation equations for the coordinates of an event in two inertial reference frames as given by x′ = γ(x–vt) vx t′ = γ t– 2 c 1 where γ = v2 1– 2 c

that Lorentz transformation equations lead to the relativistic velocity addition equation as given by u–v u′ = uv 1– 2 c

that the space–time interval Δs between two events is an invariant quantity as given by (Δs)2 = (cΔt)2–(Δx)2

that the angle between the world line of a moving particle and the time axis on a space–time diagram v is related to the particle’s speed as given by tan θ = c

that muon decay experiments provide experimental evidence for time dilation and length contraction.

Galilean and special relativity

The particulate nature of matter

molecular theory in solids, liquids and gases

that Kelvin and Celsius scales are used to express temperature

that the change in temperature of a system is the same when expressed with the Kelvin or Celsius scales

3 that Kelvin temperature is a measure of the average kinetic energy of particles as given by Ek = kBT 2

that the internal energy of a system is the total intermolecular potential energy arising from the forces between the molecules plus the total random kinetic energy of the molecules arising from their random motion

that temperature difference determines the direction of the resultant thermal energy transfer between bodies

that a phase change represents a change in particle behaviour arising from a change in energy at constant temperature

quantitative analysis of thermal energy transfers Q with the use of specific heat capacity c and specific latent heat of fusion and vaporization of substances L as given by Q = mcΔT and Q = mL

that conduction, convection and thermal radiation are the primary mechanisms for thermal energy transfer

conduction in terms of the difference in the kinetic energy of particles

quantitative analysis of rate of thermal energy transfer by conduction in terms of the type of material ΔQ ΔT and cross-sectional area of the material and the temperature gradient as given by = kA Δt Δx

qualitative description of thermal energy transferred by convection due to fluid density differences

quantitative analysis of energy transferred by radiation as a result of the emission of electromagnetic waves from the surface of a body, which in the case of a black body can be modelled by the Stefan- Boltzmann law as given by L = σAT 4 where L is the luminosity, A is the surface area and T is the absolute temperature of the body

L luminosity L of a body as given by b = 4πd2

the emission spectrum of a black body and the determination of the temperature of the body using Wien’s displacement law as given by λmaxT = 2 .

Thermal energy transfers

emissivity as the ratio of the power radiated per unit area by a surface compared to that of an ideal power radiated per unit area black surface at the same temperature as given by emissivity = σT 4

albedo as a measure of the average energy reflected off a macroscopic system as given by total scattered power albedo = total incident power

that Earth’s albedo varies daily and is dependent on cloud formations and latitude

that the incoming radiative power is dependent on the projected surface of a planet along the S direction of the path of the rays, resulting in a mean value of the incoming intensity being 4

that methane CH4, water vapour H2O, carbon dioxide CO2, and nitrous oxide N2O, are the main greenhouse gases and each of these has origins that are both natural and created by human activity

the absorption of infrared radiation by the main greenhouse gases in terms of the molecular energy levels and the subsequent emission of radiation in all directions

that the greenhouse effect can be explained in terms of both a resonance model and molecular energy levels

that the augmentation of the greenhouse effect due to human activities is known as the enhanced greenhouse effect.

Greenhouse effect

F pressure as given by P = where F is the force exerted perpendicular to the surface A

N the amount of substance n as given by n = where N is the number of molecules and NA is the NA Avogadro constant

that ideal gases are described in terms of the kinetic theory and constitute a modelled system used to approximate the behaviour of real gases

that the ideal gas law equation can be derived from the empirical gas laws for constant pressure, PV constant volume and constant temperature as given by = constant T

the equations governing the behaviour of ideal gases as given by PV = NkBT and PV = nRT

that the change in momentum of particles due to collisions with a given surface gives rise to pressure in gases and, from that analysis, pressure is related to the average translational speed of molecules as 1 given by P = ρv2 3

the relationship between the internal energy U of an ideal monatomic gas and the number of 3 3 molecules or amount of substance as given by U = NkBT or U = RnT 2 2

the temperature, pressure and density conditions under which an ideal gas is a good approximation of a real gas.

Gas laws

that the first law of thermodynamics as given by Q = ΔU + W results from the application of conservation of energy to a closed system and relates the internal energy of a system to the transfer of energy as heat and as work

that the work done by or on a closed system as given by W = PΔV when its boundaries are changed can be described in terms of pressure and changes of volume of the system

3 3 that the change in internal energy as given by ΔU = Nk ΔT = nRΔT of a system is related to the 2 B 2 change of its temperature

that entropy S is a thermodynamic quantity that relates to the degree of disorder of the particles in a system

that entropy can be determined in terms of macroscopic quantities such as thermal energy and ΔQ temperature as given by ΔS = and also in terms of the properties of individual particles of the T system as given by S = kB ln Ω where kB is the Boltzmann constant and Ω is the number of possible microstates of the system

that the second law of thermodynamics refers to the change in entropy of an isolated system and sets constraints on possible physical processes and on the overall evolution of the system

that processes in real isolated systems are almost always irreversible and consequently the entropy of a real isolated system always increases

that the entropy of a non-isolated system can decrease locally, but this is compensated by an equal or greater increase of the entropy of the surroundings

that isovolumetric, isobaric, isothermal and adiabatic processes are obtained by keeping one variable fixed

that adiabatic processes in monatomic ideal gases can be modelled by the equation as given by 5 PV 3 = constant

that cyclic gas processes are used to run heat engines

that a heat engine can respond to different cycles and is characterized by its efficiency as given by useful work η= input energy

that the Carnot cycle sets a limit for the efficiency of a heat engine at the temperatures of its heat Tc reservoirs as given by ηCarnot = 1– .

Thermodynamics

chemical cells and solar cells as the energy source in circuits

that circuit diagrams represent the arrangement of components in a circuit

Δq direct current (dc) I as a flow of charge carriers as given by I = Δt

that the electric potential difference V is the work done per unit charge on moving a positive charge W between two points along the path of the current as given by V = q

the properties of electrical conductors and insulators in terms of mobility of charge carriers

V electrical resistance R as given by R = I

the ohmic and non-ohmic behaviour of electrical conductors, including the heating effect of resistors

V2 electrical power P dissipated by a resistor as given by P = IV = I 2R = R

the combinations of resistors in series and parallel circuits

that electric cells are characterized by their emf ε and internal resistance r as given by ε = I(R + r)

that resistors can have variable resistance.

Current and circuits

Wave behaviour

the defining equation of simple harmonic motion as given by a = –ω2 x

a particle undergoing simple harmonic motion can be described using time period T , frequency ƒ, angular frequency ω, amplitude, equilibrium position, and displacement

1 2π the time period in terms of frequency of oscillation and angular frequency as given by T = = ƒ ω

m the time period of a mass–spring system as given by T = 2π k

l the time period of a simple pendulum as given by T = 2π g

a qualitative approach to energy changes during one cycle of an oscillation.

that a particle undergoing simple harmonic motion can be described using phase angle

that problems can be solved using the equations for simple harmonic motion as given by x = x0 sin (ωt + ϕ) v = ωx0 cos (ωt + ϕ)

Simple harmonic motion

transverse and longitudinal travelling waves

wavelength λ, frequency ƒ, time period T , and wave speed v applied to wave motion as given by λ v = ƒλ = T

the differences between mechanical waves and electromagnetic waves.

Wave model

that waves travelling in two and three dimensions can be described through the concepts of wavefronts and rays

wave behaviour at boundaries in terms of reflection, refraction and transmission

wave diffraction around a body and through an aperture

wavefront-ray diagrams showing refraction and diffraction

Snell’s law, critical angle and total internal reflection

n1 sin θ2 v2 Snell’s law as given by = = where n is the refractive index and θ is the angle between the n2 sin θ1 v1 normal and the ray

that double-source interference requires coherent sources

the condition for constructive interference as given by path difference = nλ

1 the condition for destructive interference as given by path difference = (n + )λ 2

λD Young’s double-slit interference as given by s = where s is the separation of fringes, d is the d separation of the slits, and D is the distance from the slits to the screen.

λ single-slit diffraction including intensity patterns as given by θ = where b is the slit width b

that the single-slit pattern modulates the double slit interference pattern

interference patterns from multiple slits and diffraction gratings as given by nλ = d sin θ.

Wave phenomena

the nature and formation of standing waves in terms of superposition of two identical waves travelling in opposite directions

nodes and antinodes, relative amplitude and phase difference of points along a standing wave

standing waves patterns in strings and pipes

the nature of resonance including natural frequency and amplitude of oscillation based on driving frequency

the effect of damping on the maximum amplitude and resonant frequency of oscillation

the effects of light, critical and heavy damping on the system.

Standing waves and resonance

the nature of the Doppler effect for sound waves and electromagnetic waves

the representation of the Doppler effect in terms of wavefront diagrams when either the source or the observer is moving

the relative change in frequency or wavelength observed for a light wave due to the Doppler effect where the speed of light is much larger than the relative speed between the source and the observer Δƒ Δλ v as given by = ≈ ƒ λ c

that shifts in spectral lines provide information about the motion of bodies like stars and galaxies in space.

the observed frequency for sound waves and mechanical waves due to the Doppler effect as given by:

Doppler effect

Fields

m1m2 Newton's universal law of gravitation as given by F = G for bodies treated as point masses r2

conditions under which extended bodies can be treated as point masses

that gravitational field strength g at a point is the force per unit mass experienced by a small point F M mass at that point as given by g = =G 2 m r

that the gravitational potential energy Ep of a system is the work done to assemble the system from infinite separation of the components of the system

m1m2 the gravitational potential energy for a two-body system as given by Ep = –G where r is the r separation between the centre of mass of the two bodies

that the gravitational potential V g at a point is the work done per unit mass in bringing a mass from M infinity to that point as given by V g = –G r

ΔV g the gravitational field strength g as the gravitational potential gradient as given by g = – Δr

the work done in moving a mass m in a gravitational field as given by W = mΔV g

equipotential surfaces for gravitational fields

the relationship between equipotential surfaces and gravitational field lines

2GM the escape speed vesc at any point in a gravitational field as given by vesc = r

GM the orbital speed vorbital of a body orbiting a large mass as given by vorbital = r

the qualitative effect of a small viscous drag force due to the atmosphere on the height and speed of an orbiting body.

Gravitational fields

the direction of forces between the two types of electric charge

q1q2 1 Coulomb’s law as given by F = k for charged bodies treated as point charges where k = r 2 4πε0

Millikan’s experiment as evidence for quantization of electric charge

that the electric charge can be transferred between bodies using friction, electrostatic induction and by contact, including the role of grounding (earthing)

F the electric field strength as given by E = q

the relationship between field line density and field strength

V the uniform electric field strength between parallel plates as given by E = d

the electric potential energy Ep in terms of work done to assemble the system from infinite separation

q1q2 the electric potential energy for a system of two charged bodies as given by Ep = k r

that the electric potential is a scalar quantity with zero defined at infinity

that the electric potential V e at a point is the work done per unit charge to bring a test charge from kQ infinity to that point as given by V e = r

ΔV e the electric field strength E as the electric potential gradient as given by E = – Δr

the work done in moving a charge q in an electric field as given by W = qΔV e

equipotential surfaces for electric fields

the relationship between equipotential surfaces and electric field lines.

Electric and magnetic fields

the motion of a charged particle in a uniform electric field

the motion of a charged particle in a uniform magnetic field

the motion of a charged particle in perpendicularly orientated uniform electric and magnetic fields

the magnitude and direction of the force on a charge moving in a magnetic field as given by F = qvB sin θ

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Simple harmonic motion

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