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EMPOWERING STUDENTS TO REACH THEIR PEAK POTENTIAL DEFINITIONS + 65 8768 7651 [email protected] @learnatzenith Buona Vista / Potong Pasir / Tan Kah Kee / Paya Lebar/ Marymount/ Tampines ...

EMPOWERING STUDENTS TO REACH THEIR PEAK POTENTIAL DEFINITIONS + 65 8768 7651 [email protected] @learnatzenith Buona Vista / Potong Pasir / Tan Kah Kee / Paya Lebar/ Marymount/ Tampines  Measurements Homogeneity of Equations: For an equation to be homogeneous, every term on both sides of the equal sign of the equation should have the same units. Systematic Errors: Systematic errors result in all readings or measurements being always smaller or always larger than the true value by a fixed amount. Random Errors: Random errors result in readings or measurements being scattered about a mean value. Accuracy: Accuracy is the degree of closeness of average value of the measurements to the true value. It is affected by systematic error. Precision: Precision is the degree of agreement between repeated measurements of the same quantity. It is affected by random error. Scalar: A scalar quantity has magnitude only. Vector: A vector quantity has both magnitude and direction.  Kinematics Distance: The length of path followed by an object. Displacement: The distance moved in a specified direction from a reference point. Speed: The instantaneous speed of an object is defined as the rate of change of distance travelled with respect to time. Average Speed: Average speed refers to the distance travelled over total time taken. Velocity: The instantaneous velocity of an object is defined as the rate of change of displacement with respect to time. Average Velocity: Average velocity refers to the change in displacement over time taken. Acceleration: The instantaneous acceleration of an object is defined as the rate of change of velocity with respect to time. Average Acceleration: Average acceleration refers to the change in velocity over time taken.  Dynamics Newton’s 1st Law of motion: A body continues in its state of rest or uniform motion in a straight line, unless a resultant external for acts on it. Inertia: The inertia of a body can be described as its reluctance to start moving or to change its motion once it has started. The mass of a body is a measure of its inertia. Weight: The Weight of an object is a measure of the gravitational force that the Earth exerts on the object. Equilibrium: The 2 conditions of equilibrium are: The resultant force in all directions is zero. The resultant torque about any axes is zero. Newton’s 3rd Law of motion: If a body A exerts a force on body B, then body B exerts an equal but opposite force of the same type on body A. Momentum: The momentum of a body is defined as the product of its mass, m and its velocity, v. It acts in the same direction as the velocity. Newton’s 2nd Law of motion: The rate of change of momentum of a body is directly proportional to the resultant force acting on it and occurs in the direction of the force. Impulse: Impulse is defined as the product of a force F acting on an object and the time ∆t for which the force acts. Conservation of momentum: The total momentum of a system remains constant, provided that the net external force acting on the system is zero. Elastic Collision: Collision in which both total momentum and total kinetic energy are conserved Inelastic Collision: Collision in which total momentum is conserved but total kinetic energy is not conserved Perfectly Inelastic Collision: Collision in which total kinetic energy is not conserved and the particles stick together after collision so that their final velocities are the same. Total momentum is conserved. Head-on Collision: Collision in which the centre of mass of the objects are collinear before and after the collision.  Forces Hooke’s Law: The extension of a spring is proportional to the applied load if the limit of proportionality is not exceeded. Density: Density of a substance is defined as its mass per unit volume. Pressure: Pressure is defined as the force per unit area, where the force is acting at right angles to the area. Upthrust: Upthrust is the vertical upward force exerted on a body by a fluid when it is fully or partially submerged in the fluid, due to the difference in fluid pressure where the pressure at the bottom is larger than the pressure at the top. Archimedes Principle: It states that the upthrust on a submerged object is equal to the weight of fluid displaced by the object. Equilibrium: The 2 conditions of equilibrium are: The resultant force in all directions is zero. The resultant torque about any axes is zero. Principle of Moments: For a body to be in rotational equilibrium, the sum of all the clockwise moments about any point must be equal to the sum of all the anticlockwise moments about the same point. Moment: The moment of a force about a point is defined as the product of the force and the perpendicular distance from the point to the line of action of the force. A couple: A couple consists of a pair of equal and opposite parallel forces whose lines of action do not coincide. Torque of a couple: It is defined as the product of one force and the perpendicular distance between the 2 forces. Centre of Gravity: The centre of gravity of a body is the point at which its weight of the body appears to act.  Work, Energy, Power Work Done: The work done by a force F is the product of the force and the displacement, S in the direction of the force. Joule: The joule is the work done by a force of 1 N on an object when it is displaced by 1 m in the direction of the force. Principle of Conservation of Energy: The principle of conservation of energy states that the total energy of an isolated system is constant. Energy can be transformed or transferred, but the total amount of energy in any isolated system must remain constant. Power: Power is defined as the rate of work done or energy conversion with respect to time.  Circular Motion Angular Displacement: It is the angle an object makes with respect to a reference line. The radian: The radian is the angle subtended by an arc length equal to the radius of the arc. Angular Velocity: Angular velocity of a body is defined as the rate of change of its angular displacement with respect to time. Period: The period of an object in a circular motion is the time taken for it to make one complete revolution. Frequency: The frequency of an object in circular motion is the number of complete revolutions made per unit time.  Gravitational Field Newton’s Law of Gravitation: It states that two point masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Gravitational Field: A gravitational field is a region of space in which a mass placed in that region experiences a gravitational force. Gravitational Field Strength: The gravitational field strength at a point in space is defined as the gravitational force experienced per unit mass at that point. Gravitational Potential Energy: The gravitational potential energy is defined as the work done by external agent to bring a small test point mass from infinity to that point in the field without acceleration. Gravitational Potential: The gravitational potential at a point in the gravitational field is defined as the work done per unit mass by an external agent to bring a small test point mass from infinity to that point in the field without acceleration. Geostationary Satellite: A geostationary satellite is one that remains at a fixed position relative to any point on the Earth’s surface. It satisfies the following conditions: Its orbital period is the same as that of the Earth about its axis of rotation (24 hrs), its direction of rotations is the same as that of Earth about its axis of rotation (eastwards), it lies above the Equator.  Oscillations Simple Harmonic Motion: It is the motion of a particle about a fixed point such that its acceleration is directly proportional to its displacement from the equilibrium point and the direction of the acceleration is always in the opposite directions of the particle’s displacement. Angular Frequency: It is the rate of change of phase angle of the oscillation. Amplitude: Amplitude is the magnitude of the maximum displacement of a particle from its equilibrium position. Period: Period is the time taken for one complete oscillation. Frequency: Frequency is the number of oscillations per unit time. Free Oscillations: Free oscillation occurs when an object oscillates with no resistive and driving force acting on it. Its total energy and amplitude remain constant with time. Damped Oscillations: A damped oscillation is where the total energy of oscillations decreases due to the presence of dissipative forces like drag. Light Damping: Light damping results in oscillations whereby the amplitude decays exponentially with time. The frequency of oscillations is slightly smaller than the undamped frequency. Critical Damping: Critical Damping results in no oscillation and the system returns to the equilibrium position in the shortest time. Heavy Damping: Heavy Damping results in no oscillation and the system takes a long time to return to its equilibrium position. hi Forced Oscillations: Forced oscillations are where an external periodic driving force is supplied to the oscillating system. Resonance: Resonance is a phenomenon where the driving frequency matches the natural frequency of the oscillating system. The system responds at a maximum amplitude of oscillation. At resonance there is maximum transfer of energy from the driver to the oscillating system.  Wave Motion Progressive Wave: A wave is a disturbance that travels through a medium from one location to another location. A progressive wave transfers energy from one point to another without the transfer of matter. Displacement: Displacement of a particle on a wave is the distance is travelled in a specific direction from its equilibrium position. Amplitude: Amplitude of a wave is the magnitude of the maximum displacement of a particle in the wave from its equilibrium position. Period: Period of a wave is the time taken for a particle of a wave to complete one oscillation. (For a progressive wave, the period is also the time taken for the waveform to travel a distance of one wavelength) Frequency: Frequency of a wave is the number of oscillations per unit time made by a particle of a wave. Wavelength: The wavelength of a wave is the distance between two consecutive points which are in phase. (2 successive crests or 2 successive troughs) Speed of a wave: The speed of a wave is the distance travelled by the wave over the time taken. Phase: The phase of a particle in a wave is the stage of motion of the particle, usually expressed as an angle in radians. Phase difference: Phase difference between 2 particles in a wave of 2 waves is the fraction of a cycle by which one is ahead of the other, usually expressed as an angle in radians. Wavefront: It is a line or surface joining points on a wave that are in phase. The wave travels in a direction that is perpendicular to the wavefront. Wave Intensity: The intensity of of a wave is defined as the rate of transfer of energy per unit area normal to the direction of wave propagation. Point Source: A point source is which waves are emitted radially in all directions. Transverse Waves: A transverse wave is one in which its particles oscillate in a direction perpendicular to the direction of energy transfer. Longitudinal Waves: A longitudinal wave is one in which its particles oscillate in a direction parallel to the direction of energy transfer. Polarization: Polarization is a phenomenon whereby the oscillations of a transvers wave are restricted to a single plane. Malus’ Law: Malus’s law states that the intensity of a beam of plane-polarized light after passing through a polarizer varies with the square of the cosine of the angle through which the polarizer is rotated from the position that gives the maximum intensity.  Superposition Principle of Superposition: The principle of superposition states that when two or more waves of the same kind meet at a point in space, the resultant displacement at that point is equal to the vector sum of the displacements of the individual waves at that point. Stationary wave: A stationary wave results form the superposition of two progressive waves of the same frequency, amplitude and speed, travelling along the same line but in opposite directions. Diffraction: Diffraction is the spreading of waves after passing through an aperture or round an obstacle. The extent of diffraction depends on the relative sizes of the slit width and the wavelength of the wave. Coherence: When waves or sources are said to be coherent, they have the same frequency and a constant phase difference. Interference: Interference is the superposition of two or more coherent waves to give a resultant wave whose resultant amplitude is give by the principle of superposition. Constructive Interference: Constructive Interference occurs when 2 waves arrive at the same point with a phase difference of zero, resulting in a maximum resultant amplitude. Destructive Interference: Destructive Interference occurs when 2 waves arrive at the same point with a phase difference of 𝜋 rad, resulting in a minimum resultant amplitude. Conditions for observable interference: 1. The waves must be coherent (same frequency and constant phase difference) 2. The waves must have approximately the same amplitude 3. The waves must overlap and be of the same type 4. For transverse waves, they must be unpolarized or polarized in the same plane Path difference: It is the difference in the distances that each wave travels from its source to the point where the 2 waves meet. Rayleigh criterion: Two images are said to be just resolved when the angular separation satisfies the Rayleigh criterion. When this happens, the peak intensity of one image lies on the first minimum of the other image.  Thermal 1: Temperature and Ideal Gas Heat: Heat is the energy transferred between 2 objects because of the temperature difference between them. Thermal Equilibrium: Thermal equilibrium occurs when 2 objects that are in thermal contact with each other and they are at the same temperature, there is no net flow of heat between the 2 objects. The Zeroth Law of Thermodynamics: If objects A and B are each in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other. Ideal Gas: An ideal gas is a gas which obeys the equation of state pV = nRT where p is pressure of the gas, V is the volume of the gas, T is the thermodynamic temperature and n is the number of moles of the gas at all pressure, volume and temperature. Mole: 1 mole of a substance is the amount of substance that contains a number of particles equal to the Avogrado’s constant.  Thermal 2: First Law of Thermodynamics Heat Capacity: It is the quantity of heat required to produce a unit temperature rise of the body without a change in phase of the body. Specific Heat Capacity: It is the quantity of heat required to produce a unit temperature rise of the body per unit mass without a change in phase of the body. Specific Latent Heat of Fusion: It is the quantity of heat required to convert a unit mass of solid to liquid without a change of temperature. Specific Latent Heat of Vaporization: It is the quantity of heat required to convert a unit mass of liquid to gas without any change of temperature. Internal Energy: The internal energy of a system is determined by the state of the system. It can be expressed as the sum of random distribution of microscopic kinetic energies and potential energies of all molecules of the system First Law of Thermodynamics: The First Law of Thermodynamics states that in a closed system, the increase in the internal energy of a system is equal to the sum of the heat supplied to the system and the work done on the system. The internal energy of a system depends only on its state.  Current of Electricity and DC Electric Current: The electric current is defined as the rate of flow of charges. Coulomb: One coulomb is defined as the amount of electric charges that passes through a point in one second when there is a constant current of one ampere. Potential Difference: The potential difference between two points in a circuit is defined as the amount of electrical energy per unit charge that is converted to other forms of energy when charges pass from one point to the other. The volt: One volt is the potential difference between two points in a circuit when one joule of electrical energy is converted to other forms of energy as one coulomb of charge passes through from one point to the other. Electromotive Force: The EMF of a source is defined as the amount of electrical energy per unit charge that is converted from other forms of energy to drive charges around a complete circuit. Resistance: The resistance of a conductor is defined as the ratio of the potential difference across it to the current flowing through it. The Ohm: One ohm is the resistance of a conductor when a potential difference of one volt across it causes a current of one ampere to flow through it. Ohm’s Law: Ohm’s Law states that the current through a metallic conductor is proportional to the potential difference across its ends under constant physical conditions like temperature.  Electric Field Coulomb’s Law: Coulomb’s Law states that the electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Electric Field: An electric field is a region of space in which a charge placed in that region experiences an electric force. Electric Field Strength: The electric field strength at a point is defined as the electric force exerted per unit positive charge placed at that point in the field. Electric Potential: The electric potential at a point is defined as the work done per unit positive charge by an external agent in bringing a small test point positive charge from infinity to that point without acceleration. Electric Potential Energy: The electric potential energy is defined as the work done by external agent to bring the charge from infinity to the point without acceleration.  Electromagnetism Magnetic Field: A magnetic field is a region of space where a magnetic material, a current-carrying conductor or a moving charge experiences a magnetic force. Magnetic Flux Density: The magnetic flux density of a magnetic field is numerically equal to the magnetic force per unit length of a long straight conductor carrying a unit current placed at right angles to the magnetic field. The magnetic force acts in a direction perpendicular to both the current and the magnetic field. The tesla: 1 tesla is the uniform magnetic flux density which acting normally to a long straight wire carrying current of 1 ampere, causes a magnetic force per unit length of 1 newton per metre acting on the wire.  Electromagnetic Induction Faraday’s Law: Faraday’s Law of electromagnetic induction states that the induced emf is proportional to the rate of change of magnetic flux linkage. Magnetic Flux: The magnetic flux is the product of the magnetic flux density and the area normal to the magnetic flux density. Magnetic Flux Linkage: The magnetic flux linkage of a coil is the product of the magnetic flux passing through the coil and the number of turns on the coil. The weber: The weber is defined as the magnetic flux through an area of 1m 2 when the magnetic flux density perpendicular to the area is 1 T. Lenz’s Law: Lenz’s law states that the direction of the induced emf is such that if an induced current flows, it must flow in such a way to produce an induced magnetic field to oppose the change in the magnetic flux linkage.  Alternating Currents Alternating current: A current in which its direction changes periodically. Root-mean-square value: The root-mean-square value of the alternating current or voltage is that value of the steady direct current or voltage that will dissipate energy at the same rate as the mean power dissipated by an a.c in a given resistor. Ideal Transformer: An ideal transformer is one in which there is no energy loss when stepping up or down the primary emf.  Quantum Physics Photoelectric Effect: The photoelectric effect is the phenomenon in which electrons are emitted from a metal surface when the incident electromagnetic radiation of frequency higher than the threshold frequency is incident on the surface. Observations of the Photoelectric Effect: 1) Existence of threshold frequency 2) Instantaneous emission of photoelectrons 3) Stopping potential is independent of intensity of incident EM radiation but dependent on frequency. Photon: A photon is a quantum of electromagnetic radiation whose energy, E is equal to hf, where h is the planck’s constant and f is the frequency of electromagnetic radiation. Work function: The work function of a metal is defined as the minimum amount of energy required for a free electron to escape from the surface of the metal. Threshold frequency: It is the minimum frequency of incident radiation required to cause the emission of photoelectrons from metal surface. Ionization energy: The minimum energy required to remove the outermost electron from the atom. Heisenberg Uncertainty Principle: It states that the product of the uncertainty of measurement of the position and momentum of a particle can never be smaller than the planck’s constant, h.  Nuclear Physics Nucleons: Nucleons refer to the protons and the neutrons in the atomic nucleus. Nuclei: Plural of nucleus. Nucleon number: The total number of neutrons and protons in the nucleus. Atomic number: The number of protons in the nucleus. Neutron number: The number of neutrons in the nucleus. Nuclide: It is a particular nucleus with a specified number of protons and neutrons. Isotope: Nuclei of atoms of a particular element containing the same number of protons but different number of neutrons. Atomic mass unit, u: It is defined as 1/12th of the mass of a carbon-12 atom. Mass defect: The mass defect is the difference between the total mass of the separated nucleons and the mass of the nucleus. Binding energy: Binding energy is the energy required to separate a nucleus into its constituent protons and neutrons such that they are separated to infinity. Binding energy per nucleon: It is the average energy per nucleon needed to separate a nucleus into its constituent nucleons. Nuclear Fission: It is the splitting of a nucleus of high nucleon number into 2 smaller nuclei of approximately equal mass with the release of energy. Nuclear Fusion: It is the building up of a larger nucleus from 2 nuclei of low nucleon number, with the release of energy. Radioactive decay: It is a spontaneous and random process where an unstable nucleus changes into a more stable nucleus, emitting radiation or particles as it does so. Spontaneous decay: A spontaneous decay means that the process is not triggered by any external factors (both physical and chemical) and the rate of decay is unaffected by environmental conditions. Random decay: A random decay means that is it impossible to predict which nucleus or when a particular nucleus will decay, while the probability of decay per unit time is constant and same for all nuclei in the sample. Decay law: For a large number of nuclei, the rate at which a particular decay process occurs in a radioactive sample is proportional to the number of undecayed radioactive nuclei present. Half-life: It is the average time taken for the activity of a sample of the radioactive nuclide to halve. Activity: It is the number of nuclear disintegrations per unit time. Decay constant: It is the probability per unit time that a nucleus will decay. Count rate: It is the rate at which emissions from a radioactive source is detected.