Physical units and vector

1. Physical units and vector A. Physical Quantities and Units • Any number that is used to describe a physical phenomenon quantitatively is called a physical quantity. • For example, two physical quantities that describe you are your weight and your height.

2. 1. Fundamenthal Physical Quantities • Some physical quantities are so fundamental that we can define them only by describing how to measure them. Two examples are measuring a distance by using a ruler and measuring a time interval by using a stopwatch.

3. In mechanics, the three basic quantities are length, mass, and time. • All other quantities in mechanics can be expressed in terms of these three. • OtherSI standards established by the committee are those for temperature (the kelvin),electric current (the ampere), luminous intensity (the candela), and the amount ofsubstance (the mole).

4. In our study of mechanics we shall be concerned only withthe units of length, mass, and time.

5. The meter (m) is defined as the distance traveled by light in vacuum during a time of 1/299 792 458second • The kilogram (kg), is defined as the mass of a specific platinum–iridium alloy cylinder kept at the International Bureau ofWeights and Measures at Sèvres, France. • The second (s), is defined as 9 192631 770 times the period of vibration of radiation from the cesium-133atom.

6. 2. Derived Physical Quantities • In other cases we define a physical quantity by describing how to calculate it from other quantities that we can measure. Thus we might define the average speed of a moving object as the distance traveled (measured with a ruler) divided by the time of travel (measured with a stopwatch).

7. B. Significant figures • When physical quantities are measured, the measured values are known only towithin the limits of the experimental uncertainty. • The value of this uncertainty candepend on various factors, such as the quality of the apparatus, the skill of the experimenter, and the number of measurements performed. • When multiplying several quantities, the number of significantfigures in thefinal answer is the same as the number of significantfigures in the least accurateof the quantities being multiplied, where “least accurate” means “having thelowest number of significantfigures.” The same rule applies to division.

8. (5.4 cm)(6.3 cm) = 34 cm2 correct • (5.5 cm)(6.4 cm) = 35.2 cm2, mistake and • (5.6 cm)(6.5 cm) = 36 cm2. correct

9. C. Scalar, vector and vector addition • When a physical quantity is described by a single number (magnitude), we call it a scalar quantity. • A vector quantity has both a magnitude and a direction in space. • Calculations that combine scalar quantities use the operations of ordinary arithmetic. For example, 6 kg + 3 kg = 9 kg. • Calculations that combine vector quantities use the operations of cosinus rule.

10. 1. Vector addition vector addition obeys the commutative law.

11. 2. Vector Subtraction • We can subtract vectors as well as add them. • To see how, recall that the vector -A has the same magnitude as vector A but the opposite direction. • We define the difference A - B of two vectors A and B to be the vector sum of A and -B

12. D. Vector component

13. E. Unit vectors and Vector Addition 1. Unit Vectors

14. 2. Vector Addition When two vectors A and B are represented in terms of their components, we can express the vector sum R using unit vectors as follows:

15. F. Scalar product of vector

16. G. Vector product of vector

17. Puspa • Intan • Anisa