Physical quantities

The foundation of physics rests upon physical quantities in terms of which the laws of physics are expressed.

Therefore, these quantities have to be measured accurately.

Among these are mass, length, time velocity, force, density, temperature, electric current, and numerous others.

Physical quantities are often divided into two categories:base quantitiesand derived quantities.

Derived quantities are those whose definitions are based on other physical quantities. Velocity acceleration and force etc. are usually viewed as derived quantities.

Base quantities are not defined in terms of other physical quantities.

The base quantities are the minimum number of those physical quantities in terms of which other physical quantities can be defined.

Typical examples of base quantities are length, mass and time.

Conversion of unis

Length1 kilometer (km)

1000 meter (m)

1 meter (m)

100 centimeter (cm)

1 centimeter (cm)

10 millimeter (mm)

1 millimeter (mm)

1000 micrometer (m)

Area1m210000 cm21 cm2100 mm2Volume1cm31ml

1000cm31000 ml = 1 liter

1m31000000 cm3Mass1 tonne (t)

1000 kilogram (kg)

1 kilogram (kg)

1000 grams (gm)

1 gram (g)

1000 milligram (mg)

Time1 day

24 hours (h)

1 hour (h)

60 minute (min)

1 minute (min)

60 second (s)

1 second (s)

1000 millisecond (ms)

1 milli second

1000 microsecond (s)

Length

Length is the distance between two points.

S.I. unit of the length is meter (m).

Initially the standard of the length was the distance between the two marks engraved on a platinum-iridium bar at 0oC kept by the International Bureau of Weight and Measure at Sevres near paris.

In 1960 the 11th general conference on weights and measures redifined meter in terms of waelength of a certain orange line in the spectrum of krypton isotope of atomic mass 86.

Note:Length is a scalar quantity.

Length-Measurement

Length can be measured using micrometers, vernier calipers, rulers and measuring tapes.

Length to be measuredExampleMeasuring instrumentLong length (Several meters)

Length of the class room

Measuring tape

Medium length

Length of table

Meter rule

Short length

External or internal diameter of the test tube

Vernier calliper

Very short length

Diameter of the wire

Micrometer screwgauge

Micrometer

Micrometer is used for more accurate measurements of the small lengths. e.g measuring the diameter of a wire or thickness of a small plate.

Micrometer - Zero error

Zero error occurs when the measuring instrument registered a reading when there should be none, which cause by an incorrect position of the zero point

Zero error1. A zero error arises when the measuring instrument does not start from exactly zero.2. Zero errors are consistently present in every reading of a measurement.3. The zero error can be positive or negative.

Time

The S.I. unit of time is second.

Initially a second was taken as 1/86400 of a mean solar day of the whole year of 1900 AD.

In the General Conference on Weight and Measure in 1967 the second was redfined as"the time interval taken by 9192631770 vibrations of cesium-133 atom under specified condition".

Multiples / submultiples of time

1 day

24 hours (h)

1 hour (h)

60 minute (min)

1 minute (min)

60 second (s)

1 second (s)

1000 millisecond (ms)

1 milli second

1000 microsecond (s)

Stop-clock

It is a specially designed watch by which time of an event can be measured accurately in minutes and seconds.

It consists of two hands , a small minutes hand and a long second hand. Both the hands are set at zero by pressing the button "Reset".

When the second handle completes one rotation equal to sixty seconds , the minute hand advances by one division.

When we want to start the watch we press the button "start/stop" and when we we want to stop it, we press the button again "start/stop".

This makes the position of the minutes and second hand stationary and record the time interval lapsed by noting the positions of the hands.

Standard form

Standard form is a way of writing down very large or very small numbers easily.

10 = 1000, so 5 10 = 5000

So 5000 can be written as 5 10

This idea can be used to write even larger numbers down easily in standard form.

Small numbers can also be written in standard form. However, instead of the index being positive(in the above example, the index was 3), it will be negative.

The rules when writing a number in standard form is that first you write down a number between 1 and 10, then you write 10 (to the power of a number).

12 000 m

1.2000 X 104m (to 5 sig. fig.) m

0.002 mm

2 X 10-3mm= 2 X 10-6m (to 1 sig. fig.)

0.000 002 m

2 X 10-6m (to 1 sig. fig.)

Parallalax errorParallax errorA parallax error is an error in reading an instrument due to the eye of the observer and pointer are not in a line perpendicular to the plane of the scale.

Simple pendulum

A point mass attached with an inextensible and weightless string whose other end is connected with some rigid support (e.g. stand) is called simple pendulum.

Amplitude of simple pendulum

It is the maximum displacement from the equilibrium position.

Its unit is cm (centimeter or meter).

Time period of simple pendulum

It is the time taken to complete one oscilation of the simple pendulum.

It is measured in seconds (s).

If pendulum has brought at position 'A' and then released freely, it passes through 'O' and reaches to B, then returns back and after passing through 'O' reaches at 'A'. In this way pendulum completes one oscilation.

Determination of time period:Calculate the time for ten oscilations with the help of stop watch and then use the following relation to determine the time period.

Time Period = Time taken / number of oscilations

Remember:1- Time period of simple pendulum depends only upon its length.

2- Time period is represented by T.

Frequency of simple pendulum

It is the total number of oscilations in one second.

It is measured in Hertz (Hz).

Time period and frequency are related with each other by the formula

Frequency = 1 / Time period

ORTime Period = 1 / Frequency

Mass

The mass of a body is the amount of matter in the body.

The S.I. unit of mass is kilogram (kg).

Mass can be measured with the help of spring balance.Gravitational Acceleration

The earth exerts a costant gravitational pull on a body at any point on its surface.

This gravitational pull will give an uniform acceleration to a free falling body (the body falling freely under the action of gravity ignoring air resistance), increasing its velocity by approximately 9.81 m/s(10m/s) every second.Hence the value of g is approximately 9.8m/s2(10 m/s2).

Different values of Gravitational accleration (m / s2)Sun

274.13

Mercury

3.59

Venus

8.87

Earth

9.81

Moon

1.62

Mars

3.77

Jupiter

25.95

Saturn

11.08

Uranus

10.67

Neptune

14.07

Pluto

0.42

Weight

Weight is the force of gravity on the object.

It is measured in Newtons (N).

The weight of object depends upon its mass and the gravitational field strength (gravitational acceleration).

Any mass near the surface of earth has weight due to the earth's gravitational pull.

Weight can be calculated using the equation

Weight = mass (m) X gravotational field strength (g)

w = mg

The value of the gravitational field strength on earth is 9.81 N/kg, through we roound it up to 10 N/kg or 10 m / s2to make the calculations easier.

Gravitational field is the region arround earth for any body, in which object enters will get the force of atarction towards the center of earth.

If you will stand on the moon, you will feel the gravity of the moon pulling you downward towards the center of the earth.

The gravitational field strengh on the moon is very less as compared to the earth.

On the moon gravitational field strength is 1.6 N / kg or 1.6 m / s2.

Difference between mass and weight

1. Mass is amount of matter in an object but weight is force of gravity on the object.

2. Mass is measured in kilograms but weight is measured in newtons as it is a force.

3. Mass is a scalar quantity but weight is the vector quantity.

4. Mass can be measured by using level(physical) balance while weight is measured by using spring balance.

5. Mass remains constant everywhere but weight varies from place to place.

For example if your weight on earth is 500 N so your mass is 50 kg.If you stand on moon still your mass would be 50 kg, but your weight would be 80N only because g = 1.6 N/kg or 1.6 m / s2on moon.

Spring balance

A spring balance can be used to determine the mass of the objects. The upper end of the spring is hung from a hook and the spring is stetched by the weight of the pan attached to its lower end.

The scale then can be adjusted so that the pointer is aligned with the zero mark.

The balance can be graduated by placing known mass in the pan.

If the spring balance shows 30 N then the mass would beW / g = 30 / 10 = 3 kg, Where g is the acceleration due to gravity.

If this balance is moved to the moon the weight would be less and spring would not stretch so far.

In fact the pointer would indicate a weight of 4.8 N (Because the value of g on the moon is 1.6 m / s2, which is the 1 / 6thof the gravitational acceleration of earth)

So spring balance measures the weight of the object in Newtons.

Remember:Mass of the object remains same every where (either on the moon or the earth)Density

Density of a substance is defined as"the mass of substance per unit volume".

Density = Mass / Volume

The S.I unit of density is kg/m3or g/cm3Mass of the substance can be found by using common level balance. Volume of a substance can either be found by calculation from linear measurements or by usning measuring cylinder.

Density of water = 1 g / cm3= 1000 kg / m3

Determination of density (Regular shaped objects)

By measuring the dimentions of regular shaped object we can detremine the its volume by using mathematical formula.

Volume = Length X Width X Height

By using balance we can find mass of the object.

Putting the values of mass and volume in the following formula, we can detrmine the density of the regular shaped object

Density = mass / volume

Determination of density (Irregular shaped objects)

To determine the density of irregular shaped objects, we use displacement method to calculate the volume of the iregular shaped object.

Use the balance to find the mass (m) of object choose the measuring cylinder that will accept the object.add liquid to the cylinder to fill it enough,so that the object will be completely submerged.measure volume v1 of liquid.

Lower the object into liquid and measure the new reading V2 so volume of object is

V=V1-V2Density = mass ( m ) / volume ( V )

This method can only be used for the objects having densities greater than density of water.

Density of different materials

Denity of different materials are as under.

SubstanceDensity in g/cm3Density kg/m3Air

1.0

1.24

Fresh water

1.03

1000

Sea water

1.03

1030

Wood

0.5-1.3

500-1300

Magnesium

1.74

1740

Steel

7.8

7800

Mercury

13.6

13600

Silver

10.5

10500

Gold

19.3

19300

Scalar

The quantities which are completely specified by their magnitude (a number and a unit associated with it) , are called scalar quantities.

Examples: Distance

Speed

Time

Energy

Resistance

Vector

The quantities which are completely specified by their magnitude (a number and a unit associated with it) and direction, are called vector quantities.

Examples: Displacement

Velocity

Acceleration

Force

Moment of force

Distance

It is the path followed by the body during its motion.

It is a scalar quantity. S.I. unit of distance is meter.

Displacement

It is the shortest distance from the initial point to the final point in the motion of the body.

It is a vector quantity. The direction of the displacement is always directed from initial point to the final point.

S.I. unit of displacement is meter.

Speed

It is the distance covered in unit time. It is a scalar quantity. It is measured in m/s.

Speed = Distance / Time

or

v = s / t

The average speed of the object can be determined by using the following relation

Average speed = Total distance covered / Total time taken

Velocity

The velocity of a body is a vector quantity and helps to detrmine, how fast or slow a body is moving in a given direction.

Therefore, velocity is defined as"Speed of a body in a particular diretion".

In SI Units velocity is measured in meters per second (m/s), the same as the unit of speed.

Average Velocity

average velocity = Total distant travel / Total time taken

The concept of average velocity is useful when velocity varies with time.

Uniform Velocity

A car moving at constant speed in straight line possesses uniform velocity as long as its magnitude and direction of motion remain unchanged.

Variable Velocity

If a body covers different displacement in equal time inetrvals, it is said to be moving with variable velocity.

The change in a velocity of a body may be caused due to change in its magnitude or direction or both.

A body moving in a curved or a circular path at a constant speed possesses variable velocity as its direction of motion changes continuously.

Graphs

It is a pictorial form of data.

In IGCSE Physics, we always plot the graph between two sets of values (2D graph).

Independent set of value is always taken along x-axis.

Dependent set of value is always taken along y- axis.

If graph is straight line and passes through the origin then the quantities along both the axes are proportional to each other.

Distance - time graph

Time always runs horizontally (along x-axis).

Distance always runs vertically (along y-axis).

The slope of distance time graph gives us speed.

Speed is a scalar quantity.

The unit of speed is m / s.

Speed - time graph

The area under the speed time - graph gives us distance.

Distance is a scalar quantity.

The unit if distance is meters (m).

EQUATIONS OF MOTION

When a (acceleration) is a constant:

V=u+at

S=(u+v)t/2

V2=u2+2as

S=ut+1/2at2Acceleration

A body moving with a variable velocity possesses accelaeration.

Acceleration can be defined as,"the time rate of change of velocity of a body" or "the change in velocity of a body in unit time".

If the velocity of body increases , its acceleration is positive and it is produced in the direction of the motion of the body.

On the other hand , if the velocity of the body decreases, its acceleration is negative and is produced opposite to the direction of the motion of the body. The negative acceleration is also called deceleration or retardation.

In case of a body moving in a straight line, the acceleration is produced due to change of speed. If the speed increases, the acceleration is positive and vice-versa.

Acceleration is also produced in case of change of the direction of motion.If a body is moving in a curved path at constant speed, acceleration is produced in it due to change in the diection of motion. the acceleration is directed inward at right angles to the direction of velocity.

In the present chapter, we restrict ourselves to the study of linear motion.

Average acceleration

The average accelelration of a moving body is obtained by dividing the total change in its velocity by the total time taken for this change.Thus,

Average acceleration = Total change in velocity / Total time taken

If v represents the change in velocity of a body produced in time internal t, the average acceleration a is given by,

a = v / t

In SI units velocity is expressed in metre per second and time in seconds, therefore, acceleration is expressed in m/s2.

Uniform acceleration

A body is said to be moving with a uniform acceleration if its velocity changes by equal amounts in equal intervals of time however small the intervals may be.

The uniform acceleration is genarally denoted by a.

The average and instantaneous values of acceleration of a body become equal when it is moving with a uniform acceleration.

Variable acceleration:

If velocity of a moving body changes by different amount in equal intervals of time, it is said to be moving with a variable acceleration.

A body is said to possess variable acceleration if the magnitude of its acceleration is changing or its direction is changing or both.

Acceleration due to gravity

Earth pulls all the objects towards its centre.This force exerted by the earth on other objects is called gravity.

Thus the motion of bodies falling freely under the influence of this force is termed as, the motion under gravity.

The force of gravity produces uniform acceleration in the bodies falling freely. This acceleration is called acceleration due to gravity and it its denoted by the letter "g".

It is the same as gravitational field strength.

It is approximately 9.81 m / s2(in IGCSE we can use 10 m / s2) on the surface of the earth.

Acceleration - Examples

Example:A train moving with a velocity of 10 m/s accelerates uniformly to a velocity of 30 m/s in 10 s. Find the acceleration of the train.

Solution:change of velocity = v = 30 m/s - 10 m/s = 20 m/s

time taken = t =10s

acceleration = a =?

a =v / t = 20 / 10 = 2 m / s2

Acceleration - Examples

Example:Find retardation produced when a car moving at a velocity of a 108 km/h slows down uniformly to 54 km/h in 5 s.

Solution:change of velocity = v = (54 km/h) - (108km/h) = - 54 km/h

In SI units velocity is expressed in m/s therefore,

v = (-54 * 1000 m ) / 60*60 = -15 m/s (Conversion fromkm/h to m/s)

Time taken = t= 5s

a =?

using a =v / t

we get

a = (-15 m/s) / 5 s = -3 m/s2The negative sign indicates that " a" is retardation or deceleration.

Force

Force is a push or pull.

SI unit of force is kg m/s2or Newton (N)

According to the Newton's second law of motion

Force = massX acceleration

F= m a

To describe a force fully you must state the size of the force(magnitude) and also the direction in which it is trying to move the object.

The direction can be described as left, right, upwards, downwards, north, south etc.

Forces acting in one dricetion can be added to get the resultant force.

Forces acting in the opposite dricetion can be subtracted to get the resultant force.

Effect of force

Forces are measure in newtons.They take many forms and have many effects including pushing, pulling, bending, stretching, squeezing and tearing etc.

Forces can:

Change the speed of an object Change the direction of movement of an object Change the shape of an object

Friction

Friction:It is the force that tries to stop movement between touching surfaces.Friction is caused by the roughness of the two surfaces.which produces resistance to movement.

Advantages of friction: Between brake pads and a bicycle when Screws and nails remain in places due to friction In movement of car on roadDisadvantages of friction: Produces heat Parts of machines reduce size due to friction Most energy is used in overcoming friction

Balanced forces

Usually there are least two forces acting on an object.

If these two forces are balanced then the object will either be stationary or moving at a constant speed (with zero acceleration).

Unbalanced forces

If the forces acting on an object are unbalanced, then it will change its speed or direction of movement it will accelerate.When a skydiver jumps from a plane, the weight will be much greater than the opposing force caused by air resistance.

Air resistance increases as the speed of skydivers increases.Finally it will match the weight so the forces will be balanced and the speed of the skydiver will remain constant. This constant maximum speed is known as the terminal speed.

Addition of forces

If two or more forces are pulling or pushing an object in the same direction the the effect of the forces will add up.If the forces pulling it in opposite directions then the backwards forces can be subtracted.If two forces are pulling an object in different direction, then their resultant can be found by using graphs.To calculate the single (resultatnt) force we draw the two forces in the correct direction and to a scale length that is suitable. e.g.

1 cm = 10 N or 1 cm = 5 N or 1 cm = 20 N etc. (depends on the size of force)Then we can find the resultant by completing the parallelogram.

Then the resultant is the diagonal line across the parallelogram between the two forces.

This gives the direction of resultant force and the magnitude is given by the length of the line.

Newton's firts law of motion

This law states thata body at rest will remain at rest, and a body moving with uniform velocity continue to do so,unless acted on by some unbalanced external foceExplanation:A cup of tea will remain on the table unless someone remove it.

simliarly a car will continue its motion in a straight line even if its engine is off but practically this does not happen.

Because of friction, air resistance and gravitational force, the car stops after some time.

If it is possible to remove these forces, the car will continue its motion in a straight line.

Newton's second law of motion

According to this law"a force applied on a body produces acceleration in its own direction. The acceleration produced varies directly with the applied force and inversely with the mass of the body".Mathematically it is expressed asF=ma

Newton's third law of motion

This law states that"Action and reaction are equal and opposite in direction."Whenever an interaction occurs between two objects,each object exerts the same force on the others, but in the opposite direction and of the same length of time.

Each force in action reaction pairs acts only on one of the two bodies. The action and reaction forces never act on the same body.

Circular motion

Moving in a circle means that the direction of motion is changing constantly.

So, if an object is moving in a circle, it follows that there must be a force acting on it to change its direction.

Therefore we can say that the direction of force is constantly changing.

In order to move an object on a circular path,the force must always be acting towards the centre of the circle.This force which is always towards the centre of the circle is given the name of centripetal force.

This centripetal forceacts perpendicularly to the direction of motion of the object at any instant.

It can be calculated by the following formulaFc=mv2/rFc= Centripetal force is NM = mass of object in kgV = Speed of object in m/s

Circular motion - Examples

Few examples of circular motion are as under:

Moon orbiting the earthcentripetal force supplied by the gravitational force of the earth on the moon.A car turning a cornerby the sideways friction force of the road on the tyres.Being whiled in a horizontal circleby the tension force in the string.The centripetal force is always towards the centre of the circle and perpendicular to the direction in which the object is travelling at that instant.

Consider the example of stone at the end of string.

Center of mass

The centre of mass is the point where we can assume all the mass of the object is concentrated.As the gravity only acts at a single point in the object. So a single arrow on diagram can represent the weight of the object.

The centre of mass for regularly shaped objects is in the centre.

For irregular shaped objects,we can find the centre of mass by following steps.1. Hang up the object.2. Suspend a plumb line from the same place.3. Mark the position of the thread.4. The centre of mass is along the line of thread.5. Repeat the above steps with object suspended from different places.6. The centre of mass is where these lines cross.Centre of mass links stability:It is important to know where the centre of mass of a body is, as its position determines the stability of the body.

A body is stable if, when it is tilted slightly, the line of action of its weight passes through its base.

Hook's law

The law states at"the extentsion of a spring (or any elastic body) is directly proportional to the applied load (stretching force), provided that elastic limit is not excceded.The graph of load and extention is a straight line which passes through the origin.

The gradient of the line is the measure of the stiffness of the spring, which is called spring constant.

Hook's law (Elastic behaviors)

If the applied force or load is removed the spring returns to its original length.This behavior is calledelastic behavior.This behavior is upto a particular point or limitcalled elastic limit.

Hook's law (Plastic behaviors)

If the applied force or load is removed the spring does not return to its original length.This behavior is called plastic behavior.This behavior is after a particular point or limitcalled elastic limit.

Hook's law - Elastic limit

Elastic limit:If you stretch the spring too far, the line (Force-extension graph) no longer straight, and hooks law is no longer true.The point at the end of the straight line is known as the limit of proportionality or elastic limit.If the material (spring) is stretched beyond the elastic limit, there is a permanent change in its shape.

After elastic limit different materials behave differently.

Effect of applied force on the materials:1)A music wire will behave as shown in the graph. It will break shortly after the limit of proportionality is reached.

Effects of applied force on the materials

Whenever force is applied on the material, It bring the change either in its length, area or volume.Hook's lawexplains the the effect of applied force on the length of the material.

Moment of force

The turning effect of force is called moment of force.The moment of force depends on the following factors. The size (magnitude) of the force The perpendicular distance between the line of action of the force and the turning point which is called the pivot.We calculate the moment of force by using the following formula

Moment of force = force * perpendicular distance from pivot to the line of action of the forceMoment=F * d

Moment is measured in newton meters(Nm).

Priciple of moment of force

This principle states that"if a system of force is not turning (or if the system is in equilibrium) then the algebaric sum of the all clockwise moments is equal to the algebaricthe sum of all anticlockwise moments about any point".Sum of clockwise moments = sum of anticlockwise moments

Equilibrium

If a body under the action of a number of forces is at rest or moving with uniform velocity, it is said to be in equilibrium.

Conditions of equilibrium

There are two conditions of equilibrium.

First condition of equilibrium:Vector sum of all the forces acting on the object is zero.

Second condition of equilibrium:The algebaric sum of all the moment of forces acting on an object iz zero. i.e.

Sum of anticlock wise moment of forces = Sum of clock wise moment of forces