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PHYSICAL QUANTITIES AND UNITS
Introduction
Physics is the study of matter, its motion and the interaction between matter.
Physics involves analysis of physical quantities, the interaction between them and the formulation of principles to explain natural phenomena.
A physical quantity is made up of a numerical magnitude and a unit.
Making measurement is important in physics. A measurement has uncertainty or errors. Many physical quantities are vectors. Knowing basic operations such as addition and products of vector are fundamental skills required in the study of physics.
International Prototype Metre standard bar made of platinum-iridium.
This was the standard until 1960, when the new SI system used a krypton-spectrum measurement as the base.
Concept Map
• Dimensions of base quantities
• Dimensional analysis – check homogeneity – construct equations
Dimensions
• SI units
• Base quantities and units
• Derived quantities and units Base Quantities and SI Units
• Sum, scalar and vector products of vectors
• Resolving a vector to two components
Scalars and Vectors
• Calculate uncertainty in a derived quantity
• Significant figures Errors
Physical Quantities and Units
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ACE AHEAD Physics First Term
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1.1 Base Quantities and SI Units
1 A physical quantity is a property that can be measured.
2 Examples of physical quantities are: length, mass, time, speed, energy, temperature and current.
3 A physical quantity is described by a numerical value and a unit.
Example: the height of a person is 2 m. The numerical value is ‘2’
and the unit is metre (m).
4 The unit of a physical quantity is the standard size used to compare different sizes of the physical quantity. In the above example, the height of the person is two times the standard length which is the metre (m).
5 In the International System of Units (SI), seven physical quantities are chosen as fundamental or base quantities. Definition of the base units for the base quantities are given in Table 1.1.
Base quantity
Base
unit Defi nition of base unit
Length metre
(m)
Distance travelled by light in vacuum during the time interval of 1/(299 792 458) second.
Mass kilogram
(kg)
Mass of a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in Sevres, France.
Time second
(s)
The time interval for the light emitted from the cesium-133 atom to complete 9 192 931 770 oscillations.
Temperature kelvin (K)
One kelvin (1 K) = 1/273.16 of the temperature of the triple point of water.
Current ampere (A)
The constant current which, if maintained in two straight parallel conductors of infi nite length, negligible circular cross- sectional area and placed one metre apart in vacuum, would produce between these conductors a force of 2 × 10–7 newton per metre of length.
Amount of substance
mole (mol)
The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kg of carbon-12.
Luminous intensity
candela (cd)
The candela (cd) is the luminous intensity, in a given direction of a source that emits monochromatic radiation of frequency 540 × 1012 Hz and that has a radiant intensity in that direction of 1/683 watt per steradian.
Table 1.1 Base quantities in SI In 1790 the metre was fixed as
the length of the pendulum with a half-period of one second.
PHYSICS FILE
(a) List base quantities as mass (kg), length (m), time (s), current (A), temperature (K), and quantity of matter (mol) (b) Deduce units for derived
quantities
LEARNING OUTCOMES
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Summary
1 A physical quantity is a property that can be measured.
2 The unit of a physical quantity is the standard size used to compare different sizes of the physical quantity.
3 The dimension of the derived quantity is the relationship between a derived quantity and the base quantities.
4 The dimension of a physical equation is homogeneous if all the terms in the equation have the same dimension.
5 Dimensional analysis enables us to construct an equation that relates a physical quantity to the variables that are observed in experiments.
6 A scalar is a physical quantity that has only magnitude.
7 A vector has both magnitude and direction.
8 The addition of two vectors P and Q is a new vector R, (P + Q) = R which is known as the resultant vector.
9 A vector R can be resolved into two components Rx and Ry that are mutually perpendicular Rx = R cos q and Ry = R sin q
tan q = Ry
Rx R = R2x + Ry2 where q is the angle between the component Rx and the vector R.
10 The scalar product of two vectors a.b = |a||b| cos q where q is the angle between the two vectors.
11 The vector product of two vectors a × b is a vector whose magnitude is given by
|a × b| = |a||b| sin q
The direction of a × b is such that the vectors a, b and a × b form a right-hand system.
2 The diameter of a metal sphere is (5.00 ⫾ 0.01) cm, and its mass is (235 ⫾ 5) g.
(a) Calculate the percentage uncertainty in the determination of the density of the metal.
(b) Calculate the density of the metal and state its absolute uncertainty.
3 The time for 40 oscillations of a simple pendulum recorded using a stopwatch is 48.6 s. Calculate the period of the simple pendulum to the correct number of significant figures.
4 A rectangular plot of land is (118.6 ⫾ 0.1) m long and (75.26 ⫾ 0.01) m wide.
Calculate (a) the perimeter and (b) the area of the plot.
Give the uncertainty for each of the answers.
COMPANION WEBSITE
Online Test
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OBJECTIVE QUESTIONS
Focus on Exam 1
1 The dimension of angular velocity is A T–1
B L T–1 C L T–2 D L2 T–1
STPM 2005/P1/Q1
2 The tensile strength of a wire is the maximum stress on the wire just before it breaks. What is the dimension of tensile strength?
A M L–1 T–1 B M L–1 T–2 C M L T–1 D M L T–2
STPM 2007/P1/Q1
3 The unit for power is watt (W). In terms of the base SI units, W is given by
A kg m s–2 B kg m2 s–1 C kg m2 s–2 D kg m2 s–3
4 Newton’s law of gravitation states that the gravitational force F between two point masses m and M separated by a distance r is given by F = G mM
r2 . What is the SI unit for G?
A m s–2 B N m–2 s–2 C m2 kg–2 D kg–1 m3 s–2
5 Which of the following equations is dimensionally homogeneous?
A Force = mass × displacement B Work = mass × velocity C Power = force × velocity D Impulse = force × displacement 6 The possible factors that affect the speed
v of waves in the sea are r the density of sea water, h the depth of the sea, l the
wavelength and g the acceleration due to gravity. If k is a dimensionless constant, in which equation the dimension is consistent?
A v = k gl B v = k ghr C v = k g
l D v = k gl
r
7 The momentum of a body of mass m is p.
Which quantity has the same unit as p2 m? A Force
B Energy C Power D Pressure
8 Which pair contains a scalar quantity and a vector quantity?
A Work and weight B Power and energy C Impulse and momentum D Potential energy and distance
9 Forces of 10 N and 6 N act on a point.
Which of the following cannot be a possible magnitude of the resultant force?
A 3 N B 6 N C 10 N D 12 N
10 The resultant of three vectors P, Q and R is X. Which vector diagram correctly shows X = P + Q + R?
R
A X
Q P
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1 Which of the following is the dimension for pressure?
A M L–1 T–2 C M L–2 T–2
B M L T–2 D M L–1 T–1
2 The length of a strip of paper is 20.2 cm and its width is 0.925 cm. The perimeter of the strip to the correct significant figure is
A 42 cm C 42.25 cm
B 42.3 cm D 42.250 cm
3 A car and a bus pass a point P in the same direction along a road at time t = 0. The speed-time graphs of the vehicles are as shown in the figure.
Speed (m s–1)
5 10 15 20 25
Bus
Car 20 Time (s)
0 5 10 15
The bus overtakes the car after
A 5 s C 15 s
B 10 s D 20 s
4 A ball is kicked from a point P and moves off with a speed v at an angle of 45° to the ground.
It passes over the horizontal bar of a goal post which is at a height h. What is the speed v of the ball? (g is the acceleration due to gravity.)
A 1
2 gh C 2gh
B 1
2 gh D 2 gh
5 A particle P moving with a velocity 4.0 m s–1 collides elastically into another particle Q of the same mass moving with a velocity of 1.6 m s–1 in the same direction. What are the velocities of P and Q after collision?
Velocity of P Velocity of Q A 1.6 m s–1 4.0 m s–1 B 2.8 m s–1 2.8 m s–1 C 3.0 m s–1 2.6 m s–1 D 3.8 m s–1 1.8 m s–1
PHYSICS PAPER 1 Time: 1 hr 45 min
Section A (15 marks)
Answer all questions in this section.
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