H2 Physics Summary for all topics

A1 SI base units In the SI system of units, there are seven base quantities and their units. These 7 quantities are assumed to be mutually independent. Base Quantities SI Base Units Name Symbol Length metre m Mass kilogram kg Time seconds s Current ampere A Temperature kelvin K Amount of substance mole mol Luminous Intensity candela cd Derived Quantities Derived quantities are physical quantities expressed in terms of one or more bas e quantities. General rules for determining the units of derived quantities: 1) For addition / subtraction of two or more quantities, each quantity must have the SAME unit. 2) For multiplication / division, rules of algebraic multiplication and division apply. 3) Exponents (powers/indexes) are unitless. Homegeneity of Physical Equations • Each term in an homogeneous equation has the same units. • For any two quantities to be equated, added or subtracted , they must have the same dimension (or units). • Homogeneous equation may not be correct (e.g. missing terms / coefficients) but a non - homogeneous equation must be wrong. Prefixes (Order of magnitudes) Can be added to SI base units and derived units to make larger or smaller units. (e.g. 1 ms = 10−3 s, 1 km = 103 m ) Name Symbol Factor pico p × 10−12 nano n × 10−9 micro μ × 10−6 milli m × 10−3 centi c × 10−2 deci d × 10−1 kilo k × 103 mega M × 106 giga G × 109 tera T × 1012 Systematic Error & Random Error Systematic errors have the same magnitude and sign when measurements are repeated. Causes: Instrument errors (e.g. zero errors), Environmental conditions, Poor experimental techniques (e.g. parallax error). Systematic error can be eliminated if the source of the error is known. Random errors have different magnitudes and signs (i.e. varying both magnitude and direction) when measurements are repeated. Causes: Variations in environmental conditions, Irregularity of the quantity being measured, Limitation of equipment. Random error cannot be completely eliminated but can be minimised by finding the average of repeated measurements. Precision & Accuracy Precision refers to how close the repeated measured values are to each other , without regard to the true value of the quantity. Repeated measurements which are very close to one another are precise measurements. Thus an experiment which has small random errors (i.e. small spread of readings) is said to have high precision. Accuracy refers to how close a measured value is to the true value of a quantity. An experiment which has small systematic errors is said to have high accuracy. The average value is close to the true value. Errors / Uncertainties When making any measurement, there is always some uncertainty / error. Experimental uncertainty or error = Measured value – True value Absolute error / uncertainty – e.g. error / uncertainty in measuring length, Fractional error / uncertainty – e.g. Percentage error / uncertainty – e.g. General rules for recording measurement with its uncertainty (i.e. ): • Round off errors / uncertainties / absolute uncertainties to 1 s.f. (i.e. rounded to 1 s.f.) • Write the measured value to the same decimal place as its error / uncertainty / absolute uncertainty. (i.e. rounded to same d.p. as ) MEASUREMENTS

A2 Consequential Uncertainties Method 1 - Numerical Substitution 1. Find the “best” value 2. Find the “maximum” value 3. Uncertainty = max value – best value Method 2 - Formula Method Addition/Subtraction If Y = nA  mB then Y = nA + mB Multiplication/Division If or , where α, , m and n are numbers, then These rules can also “stack up”, e.g.: if , where α, , m and n are numbers, then Important: To determine the error of a quantity, always express the quantity as the subject of the equation first. Scalars & Vectors A scalar quantity is one with magnitude only. A vector quantity is one that has a magnitude and direction (e.g. displacement, velocity, acceleration, momentum, etc). Vector addition • Use to determine the resultant of two vectors. • Use parallelogram or vector triangle. Change of a vector (e.g. ) refers to final vector – initial vector. (e.g. ) Relative velocity refers to the velocity of one object relative to another moving object. Suppose body 1 has velocity and body 2 has velocity . Relative velocity of 1 with respect to 2 is represented as . Resolution of Vector into two perpendicular components: Remember: • The component on the side adjacent to the angle – cosine function • The component on the side opposite to the angle – sine function Note: 2 perpendicular vectors are independent of each other. To determine the vector sum of 3 or more vectors: 1. Identify two perpendicular axes to determine components of each vector. 2. Determine the components of each vector. 3. Determine the vector sum of each component for all vectors. 4. Find the resultant of the two net perpendicular components using Pythagoras theorem.

B1 KINEMATICS Physical Quantities Representing Motion Scalars: ▪ Distance (x) is the total length moved by an object irrespective of the direction of motion. ▪ Speed of an object is defined as the rate of change of distance travelled. → average speed x t =  → instantaneous speed dx dt= Vectors: ▪ Displacement (s) is the shortest linear distance of the position of a moving object from a given reference point. ▪ Velocity of an object is defined as the rate of change of its displacement. → average velocity s t =  → instantaneous velocity ds dt= ▪ Acceleration of an object is defined as the rate of change of its velocity. → average acceleration v t =  → instantaneous acceleration dv dt= → Acceleration can refer to increase or decrease in velocity. Negative acceleration DO NOT necessary indicate that object is slowing down. To determine if object is speeding up or slowing down (decelerating), compare the directions of the velocity and acceleration vectors. If both velocity vector and acceleration vector are in the SAME direction, object speeds up. If velocity vector and acceleration vector are in OPPOSITE direction, object slows down. Rectilinear Motion (1-D Motion) Equations of Motion (suvat) ▪ ONLY applicable for motion → in a straight line → with constant acceleration ▪ Need to be able TO DERIVE from definitions of velocity and acceleration. ▪ (1) v u at=+ (2) 22 2v u as=+ (3) 21 2s ut at=+ (4) 1()2s u v t=+ *Remember to take into account sign convention when applying these equations* Projectile Motion (2-D Motion) ▪ Object projected in a uniform gravitational field with negligible air resistance, results in a parabolic path ▪ Step 1: If you are given the initial velocity, resolve it into its x and y components. ▪ Step 2: Analyze the horizontal (x) and vertical (y) motion separately. ▪ Step 3: Recall that (i) time t links the x and y component motions (ii) ay = 9.81 m s−2 and is directed downwards (iii) at max height, vy = 0 (iv) vx = ux (since ax = 0) ▪ Step 4 : Apply the relevant equations of motion (suvat). *Remember to take sign conventions into consideration!* *Only vertical and horizontal components can be used for the equations Graphical Representations of Motion Features s – t graph v – t graph a – t graph Axes Displacement Instantaneous velocity Instantaneous acceleration Gradient Instantaneous velocity dsv dt= Instantaneous acceleration dva dt= ---- Area under graph ---- Net change in displacement Net change in velocity

C1 Moment or torque  •  = F d (find perpendicular distance or force) • Torque of a couple is product one of the forces and the perpendicular distance between the lines of action of the forces Free Body Diagram (FBD) • Draw all fo