MATA KULIAH BAHASA INGGRIS FISIKA

THE CONCEPT OF PHYSICAL QUANTITIES AND THEIR MEASUREMENTS

Measurement

Measurement is an estimation of a magnitude of some attributes of an object, such as length, time or weight, relative to a unit of measurement.

Physical quantities are characterized by:

•       a number that describes the magnitude of the quantity,

•       a unit of measure, which describes the nature of the quantity,

•       a method to perform the measurement of the physical quantity.

A physical quantity is a physical property that can be quantified. This means it can be measured and/or calculated.

1.       Length

expresses the distance or extent in space. The standard used for measurement is a distance light travels in vacuum for second 1/299.792.458               .

An object of the same length as the standard bar is said to have a length of l = 1 [m] "meter".

•       Picture: kilogram standard

Mass expresses the quantity or amount of matter. The standard is a cylinder of platinum-iridium, and an object of same mass as the standard is said to have a mass of m = 1 [kg] "kilogram".

•       Picture: atomic clock

This is a rather abstract concept which necessitates a precise definition through a measurement procedure. The standard of time has changed with time, and now an atomic clock is used for this purpose

•       The value of a physical quantity

The value of a physical quantity Q is expressed as the product of a numerical value {Q} and a physical unit [Q] .

           Q = {Q} × [Q]

•       Units of measurement

Units are standards for measurement of physical quantities.

The International System is called the SI, using the first two initials of its French name Système International d'Unités.

•       SI base units

Base Quantity	Name	Symbol
length	meter	m
mass	kilogram	kg
time	second	s
electric current	ampere	A
thermodynamic	temperature	K
amount of substance	mole	mol
luminous intensity	candela	cd

•       SI derived units

No	Derived unit	Measures	Derivation	Formal definition
1	hertz (Hz)	frequency	/s	s-1
2	newton (N)	force	kg (m/s2)	kg.m.s-2
3	pascal (Pa)	pressure	N/m2	kg.m-1.s-2
4	joule (J)	energy or work	N·m	kg.m2.s-2
5	watt (W)	power	J/s	kg.m2.s-3
6	coulomb (C)	electric charge	A.s	A.s
7	volt (V)	electric potential	W/A	kg.m2.s-3.A-1
8	farad (F)	electric capacitance	C/V	kg-1.m-2.s4.A2
9	ohm (omega)	electric resistance	V/A	kg.m2.s-3.A-2
10	siemens (S)	electric conductance	A/V	kg-1.m-2.s3.A2

•       SI prefixes

Factor	Name	Symbol	Factor	Name	Symbol
1024	yotta	Y	10−1	deci	d
1021	zetta	Z	10−2	centi	c
1018	exa	E	10−3	milli	m
1015	peta	P	10−6	micro	μ
1012	tera	T	10−9	nano	n
109	giga	G	10−12	pico	p
106	mega	M	10−15	femto	f
103	kilo	k	10−18	atto	a
102	hecto	h	10−21	zepto	z
101	deka	da	10−24	yocto	y

Dimension is the relation that describes a derived unit for a certain quantity in terms of the fundamental units.

Base Quantity	Name	Symbol	Dimensions
length	meter	m	[L]
mass	kilogram	kg	[M]
time	second	s	[T]
electric current	ampere	A	[I]
thermodynamic	temperature	K	[θ]
amount of substance	mole	mol	[N]
luminous intensity	candela	cd	[J]

Kinematics of rectilinear motion

•          mechanics

1)      Kinematics

is a branch of mechanics concerning with motions without regarding the causes of the motions

2)      Dynamics

is a branch of mechanics concerning with motions with regarding the causes of the motions

In physics, the object is called in motion if its position changes against a reference point.

Rectilinear motion is the motion with rectilinear path

The other example of the rectilinear motions

The physical quantity of rectilinear motions

1. Displacement and distance

Displacement is a change of the object’s position at a certain time.

∆x = x_final – x_initial

Distance is a length of the actual path travelled by the object during a motion.

|∆x| = |x_final – x_initial|

Example 1.2

An object moves in a line with x axis direction. The initial position of the object is in zero point. The object moves 3 meters to the right direction. Then, the object moves 2 meters to the left direction. Determine the displacement and distance of the object.

Solution

Look at the picture below.

Displacement

∆x₁ = 3 – 0 = 3 m

∆x₂ = 1 – 3 = -2 m

∆x = ∆x₁ + ∆x₂ = 3 + (-2) = 1 m

The direction is x positive.

Thus, the displacement of the object is 1 m with direction to the x axis positive.

Distance

| ∆x₁ | = |3 – 0| = 3 m

| ∆x₂ | = |1 – 3| = 2 m

| ∆x| = |∆x₁ | + |∆x₂|  = 3 + 2 = 5 m

Thus, the distance of the object is 5 m.

2. Velocity and speed

Speed is the distance travelled by an object per unit of time. Velocity is the displacement of an object per unit per time. Speed is a scalar quantity and velocity is a vector quantity.

•          velocity

1.       Average speed and average velocity

2.       Instantaneous speed and instantaneous velocity

Exploration 2.2
Do you know the speedometer? Speedometer is the instrument to measure the instantaneous speed of an object like a motorcycle or a car.
Pay attention to the speedometer when a motorcycle or a car moves. Then, answer the questions below.

1. What is the unit of speed which you find in a motorcycle or car?

    ______________________________

2. Where will the hand of the

    speedometer moves, while a

    motorcycle or a car moves faster than

    before? (to the left or to the right)

Acceleration
is a change of velocity per unit of time. Acceleration is a vector quantity. The symbol of acceleration is a.

•          Acceleration

•          Average acceleration

•          Instantaneous acceleration

Kinds of rectilinear motion

1.       Uniform rectilinear motion

is the motion in linear path with a constant velocity or speed.

The graph of uniform rectilinear motion

The area under a velocity-time graph equals the displacement.

v = tan θ

It means that, the velocity of the object will be bigger than the others if the gradient of the graph is steeper

2.       Uniformly accelerated rectilinear motion

is a motion in a linear path with a constant acceleration.

The other equations in uniformly accelerated rectilinear motion

v = v_o + at

Vertical motion

Is a kind of uniformly accelerated rectilinear motion in vertical direction.

Circular Motion

Circular motion is an object’s motion in circular path

1. Angular distance or angular displacement

Is the distance or displacement of particle in circular motion

•       2. Angular speed or velocity

is a speed or velocity in circular motion.

Two kind of angular speed or velocity:

1. Average angular speed or velocity
2. Instantaneous angular speed or velocity

•       3. Period and Frequency

The period is the time required by an object (particle) to reach a complete rotation. It means that the period is the time required by an object to move from one point (suppose A) passes through a circular path which has radius R and back to the point (suppose A).

The frequency is the sum of rotation in one second.

•       The relationship of period and frequency

•          Angular speed or velocity

Frequency

Linear speed

period

•       Exploration

Do you have a clock? There are three hands in a clock. One hand shows hour and the other shows minute and still the other shows second. How do the three hands of the clock moves? However, the stick of the hands are in the same point, but they doesn’t move together. Answer this question below.

1. Which of the three hands of the clock moves the fastest? ____________________
2. Which of the three hands of the clock moves the slowest?___________________
3. Calculate the period of the three hands in a  clock. _______________________________
4. Calculate the frequency of the three hands in a clock.____________________________

•       4. Acceleration in circular motion

Angular acceleration (α)

Tangential acceleration (α_t)

Centripetal acceleration (α_s)

The relationship of angular acceleration, tangential acceleration, and centripetal acceleration

•       Kinds of circular motion

1. Uniform circular motion

                is a motion of object at circular path with constant angular velocity (ω = constant).

•       2. Uniformly accelerated  circular motion

is the motion of an object at circular path with constant angular acceleration (α = constant).

The uniformly accelerated circular motion is analogue to the uniformly accelerated rectilinear motion

The uniformly accelerated rectilinear motion	The uniformly accelerated circular motion
v = vo + at	ω = ω0 + αt
x = x0 + v0t + ½at2	θ = θ0 + ω0t + ½αt2
v2 = v02 + 2ax	ω2 = ω02 + 2αθ

DYNAMICS AND NEWTON’S LAW

FORCE

Force is a push or a pull upon an object and resulted from the object interaction

The magnitude of force resultant from two forces F₁ and F₂

The direction of force resultant (R)

•          Kinds of force

•          Weight

•          Normal force

•          Frictional force

•          String tensional force

•       Weight is the gravitational force works on an object near the earth surface

w = mg

•       The normal force is a force which acts on the contact plane between two surfaces of the objects in contact.

If an object is placed on a smooth plane with no outside force, then the normal force is equal to the weight of the object (N = w).

•       Frictional force is a force opposing the direction of the object’s motion.

 The symbol of frictional force is f

•          Frictional force

•          Static frictional force is a frictional force exerts influence upon a resting object

•          Kinetic frictional force is a frictional force exerts influence upon a moving object

The string tensional force is the force transmitted through a string or wire when it is tightly pulled by forces acting on one end of the string.

The centripetal force is experienced by an object which is in circular motion. The centripetal force has direction toward the center of the path. The example is the car moves in circular path.

F_s = ma_s

•       Newton’s law of motion

Newton’s third law

Newton’s second law

Newton’s first law

•       Newton’s first law

“The object remains at rest or in motion with a constant velocity unless acted upon by an unbalanced force.”

ΣF = 0

•       Newton’s second law

“The acceleration of a body depends both on the force and on the mass of the body.”

ΣF = ma

•       Newton’s third law

“For every action force, there is an equal and opposite reaction force.”

F_action = -F_reaction

•       The differences of Newton’s first law and Newton’s third law

Look at the figure!

The Newton’s third law equation expresses the pair of forces acting upon two different objects (a), while the Newton’s first law equation expresses the balanced forces upon the same object (b).

•       Application of Newton’s law

1. The motion of object on a smooth plane
2. The motion of object on a rough plane
3. The motion of object on an inclined plane
4. The motion of object connected by a pulley
5. The weight of object in the lift

•       Example 4.10

Look at the following figure.

The string mass and the pulley mass are neglected, m₁ = 5 kg, m₂ = 10 kg, and g = 10 m/s². Determine the distance of m₁ when t = 1.2 second from the rest.

Solution

s = v_ot + ½at²

Because m₁ = 5 kg, m₂ = 10 kg, g = 10 m/s², t = 1.2 s, and the pulley is smooth.

m₂ > m₁

a₁ = a₂ = a

ΣF_y = ma

w₂ – w₁ = ma

m₂g – m₁g = (m₂ + m₁)a

s = v_ot + ½at² = 0 + ½ = 2.4 m

Thus, the distance of m₁ when t = 1.2 second from the rest is 2.4 m