Chapter 1: Physical Quantities & Measurement | California State University, Northridge

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California State University, Northridge
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PHYS 100A | General Physics I
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2023
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KOLEJ MATRIKULASI SELANGOR physics\akademik\1PN\SF016\ch1 1 Physical Quantities & Measurement 1.1 Physical Quantities & Units 1. Physical quantities – a quantity that can be measured 2. Basic quantity – quantity 3. Derived quantity – quantity which cannot be derived which can be expressed in from any physical quantities term of base quantity Mass, m Length,  Time, t Temperature, T Current, I Amount of substance, n Luminous intensity, IV kg m s K A mol cd 1.2 Scalars & Vectors 4. Scalar quantity is defined as a quantity with magnitude only e.g. mass, time, temperature, pressure, electric current, work, energy and etc 6. Area, A Acceleration, a Force, F Work, W m3 m s-2 N @ kg m s-1 J @ kg m2 s-1 5. Vector quantity is defined as a quantity with both magnitude & direction e.g. displacement, velocity, acceleration, force, momentum, electric field, magnetic field and etc Addition and subtraction of vectors can be done graphically/ geometrically by: 3. Prefixes - for presenting larger and smaller values eg: 1 pF  F 4700 m3  mm3 0.5 J min-1  J s-1 Prefix Multiple Symbol tera giga mega kilo deci centi milli micro nano pico   109  106  103  10-1  10-2  10-3  10-6  10-9  10-12 T G M k d c m  n p 11. Unit vector are dimensionless 12. We shall use the symbols i, j, and k to represent unit vectors pointing in the positive x, y, and z directions, respectively 13. The magnitude of each unit vector equals 1 1012 |𝑖̂| = |𝑗̂| = |𝑘̂ | = 1 14. In 2-D, let A = Axi + Ayj B = Bxi + Byj (Component vectors) and R = Rxi + Ryj (Resultant vector) So R=A+B R = (Ax + Bx)i + (Ay + By)j where Rx = Ax + Bx Ry = Ay + By And Magnitude of R = √𝑅𝑥 2 + 𝑅𝑦 2 𝑅𝑦 𝐴𝑦+𝐵𝑦 Direction, tan  = = 𝑅𝑥 7. 8. 9. The geometric method of adding vectors is not recommended whenever great accuracy is required or in 3-D problems. By use of the projections of vectors along coordinate axes (the components of the vector), we can add any vectors mathematically. The component Rx represents the projection of R along the x axis, and the component Ry represents the projection of R along the y axis. Rx = R cos  Ry = R sin  Magnitude, R = √𝑅𝑥 2 + 𝑅𝑦 2 𝑅𝑦 Direction, tan  = 𝐴𝑥+𝐵𝑥 15. Multiplication of vectors – 2 types (i) Scalar/ Dot product: A  B = AxBx + AyBy + AzBz A  B = IAIIBI cos  IAI = √𝐴𝑥 2 + 𝐴𝑦 2 + 𝐴𝑧 2 Let IBI = √𝐵𝑥 2 + 𝐵𝑦 2 + 𝐵𝑧 2 A = Axi + Ayj + Azk 𝐴𝐵 B = Bxi + Byj + Bzk cos  = |𝐴||𝐵| (ii) Vector/ Cross product: Will produce a new vector, C AB=C The direction of vector is determined by RIGHT-HAND RULE Magnitude, ICI = IA  BI = IAIIBI sin  Let A = Axi + Ayj + Azk B = Bxi + Byj + Bzk 𝑖̂ 𝑗̂ 𝑘̂ A  B = |𝐴𝑥 𝐴𝑦 𝐴𝑧| 𝐵𝑥 𝐵𝑦 𝐵𝑧 = 𝑖̂(AxBy – AyBx) – 𝑗̂(AxBz – AzBx) + 𝑘̂ (AxBy – AyBx) 16. The angle between two vectors can only be determined by using the scalar (dot) product 𝑅𝑥 10. Unit vectors – a vector with a magnitude of 1 unit in the direction of vector A http://www.netcomuk.co.uk/~jenolive/vect6.html