WEBVTT

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A formula is a recipe or a rule
for doing something and it works

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every time it gives the
relationship between different

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quantities. Some formerly a
standard formally written down

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by Mathematicians and scientists
to cover a wide range of the

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relationships between different

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quantities. Others can be made
up such as that for a washing

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powder or a magician's memory

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trick. More of that later.

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Formally, usually use variables
and letters instead of numbers,

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and that gives the relationship.
Let's have a look at.

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The formula for the area
of a circle A equals π R

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squared, where a is the
area of the circle.

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And R is the radius of
the circle.

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This formula works every time
and shows the relationship.

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So we square the radius. We
multiplied by pie and it

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gives us the area and it will
always work.

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Imagine we have a circular lawn
where the radius is 3 meters.

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And we want to know how much
turf in square meters that we

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need to order so R is equal to 3

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meters. So what we're going
to do instead of writing are

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in our formula. We're going
to write the number 3, so A

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is equal to Π * 3 squared.
Now, it's really important

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that we put the
multiplication sign back in

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as soon as we put numbers
back in our formula.

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Π * 3 squared is π
* 9, giving us 28.3.

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So the area of our.

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Lawn is going to be 28.3
meters squared, so we're

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going to need at least 29
meters squared of turf.

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There are many formerly that
relates to the area of 2D

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objects and also to the volume
of 3D solids.

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Let's have a look at one. Now
let's say we want to find the

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volume of a football.

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Now football is a sphere, so we
want the formula for the volume

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of a sphere and that's V equals
4 thirds of Π R cubed.

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And let's say that the
radius of a sphere are

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football is 10 centimeters.

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So in our formula to workout the
volume instead of writing, are

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we going to write 10
centimeters, so V equals 4

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thirds π multiplied, again
remembering to put the multiply

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symbol in and instead of are we
writing 10, so 10 cubed?

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And if we calculate all of that.

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We end up with the
volume equaling 4189, so the

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volume of the football since
the radius was in centimeters

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will be 4189 centimeters cubed.

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There are many formerly relating
to scientific principles.

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And we're going to have a look
at Newton's second law.

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And that law relates force
with mass and acceleration.

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And the formula is F equals
MA mass times acceleration.

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Let's imagine a circus artist is
going to be fired from the

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barrel. And he's going
to be fired horizontally

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and the mass of a circus
artist is 60 kilograms.

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And he's going to be fired
at an acceleration of 2.5

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meters per second squared.

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Our formula is F equals MA.

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So instead of em, we're
going to write 60.

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And instead of a, we're going to

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put 2.5. But again, because
we're putting numbers in.

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Instead of the letters, we must
remember to put the multiply

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sign back in so it'll be 60
times by 2.5.

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That gives us 150, so the
force on our circus artists is

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150 newtons. And Newton is
a unit of force.

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Let's look at an equation
of motion.

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Z equals you plus 80.

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Fee represents final speed.

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You initial speed.

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Hey, is acceleration.

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Auntie is time.

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And imagine that we've got some
values for you A&T.

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So you.

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Equal to 5.

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A is equal to two and T
is equal to 3.

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So to calculate V, the final
speed, we're going to

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substitute these numbers
instead of these letters.

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So instead of you, we write 5
instead of a. It's two, we must

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write the multiply sign because
we're now putting numbers

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instead of letters.

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And instead of T we write 3.

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Now we've got a good
opportunity here to look at

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our order of operations. If
we were to start from the

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left and work through to the
right, we would be in error

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because we should do
multiplying before we do

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addition. So a quick
reminder of our order of

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operations with Bob Mass.

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Where the B stands for brackets,
the apfa powers.

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Steve for divide
and for multiply.

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A for addition.

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And S for subtraction.

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So multiply comes before
addition, so we need to do

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2 * 3 before we do the
addition, so it's 5 + 6,

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giving us an answer of 11.

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Let's look at another equation
of motion. This time V squared

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equals U squared plus 2A S.

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Again, the final speed.

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You initial speed.

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Hey Accelleration.

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And S distance traveled.

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And imagine we've got a Cliff.

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And we throw a stone off the top
of the Cliff and we'd like to

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know the speed with which it
hits the water below.

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And the Cliff is
100 meters high.

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So we know that you
are initial speed.

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Is zero 'cause we're dropping
the stone from rest at the top?

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Our acceleration is the
acceleration due to gravity, so

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that's 9.8 meters per second

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squared. And as the distance
that it falls is 100 meters.

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So instead of the letters
in our formula, we

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substitute the numbers.

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UO

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plus two times
a 9.8 times

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S 100.

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That works out at
1960. Sophie squared is

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1960. So to calculate V,
the final speed when it

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hits the water, we need to
square root 1960 and that

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gives us an answer of 44.

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And because.

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Our units are meters per second
squared for acceleration in

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meters for the distance that
it's fallen, the velocity is 44

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meters per second.

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Another equation of motion is S
equals UT plus a half 80

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squared. What S is the distance?

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You is the initial speed.

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T is time.

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A accelerations.

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And the final to the same as

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this one time. Not so much in
this time that we have a well.

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And we want to find out
how deep the well is.

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And what we do is we drop a
stone down the well.

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Use the initial speed of the
stone is 0 because we dropped

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it. It started at rest.

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Let's say it takes 3 seconds for
the stone to hit the bottom.

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And AR acceleration is that due
to gravity of 9.8 meters per

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second squared. So instead of
writing you T&A in our formula,

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we're going to substitute and
put these values in.

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So S equals you
0 multiplied by T3.

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Plus half multiplied
by 9.8.

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Multiplied by T squared.

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So we put all the figures in.
Now we can carry out the

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calculation. 0 * 3 zero
plus half of 9.8 four point

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9 * 3 squared is 9.

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That gives an answer of 44 to
the nearest whole number. And

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because our units are meters
per second squared and

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seconds, the depth of the
world will be 44 meters.

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Let's have a look at the formula
for kinetic energy.

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Kinetic energy equals 1/2 MV

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squared. Where M represents mass
and the is the speed that the

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mass is traveling at.

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The amount of work done, kinetic
energy. Let's compare a sprinter

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running and the work that is
done by the sprinter running

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with that of a truck. So the
sprinter is mass 70 kilos.

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And the running at a speed of 10
meters per second.

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Another truck

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has a mass of 2000 kilos.

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And that's going forward at a
speed of 20 meters per second.

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So let's compare how much
work they're doing. So for

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this printer.

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The kinetic energy equals 1/2.
The mass is 70.

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The velocity is 10 squared.

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So we have 3500.

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For the truck.

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The kinetic energy again
is 1/2 instead of the M

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we write 2000.

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And instead of the V, we've got
20 to be squared.

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And that works out at 400,000.

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So the kinetic energy of
the truck is more than 100

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times greater than that of
the sprinter.

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I haven't written the units
down, but for kinetic energy

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there jewels.

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Let's look now at the formula
for the period of a pendulum

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where T equals 2π root L over G.

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What city is the period of
the pendulum?

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And that means how long the

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pendulum takes. To go from
one side of its motion to the

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other and then back again. So
that's the period.

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L is the length of the pendulum.

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And she is the acceleration.

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Due to gravity.

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Which is 9.8 meters
per second squared.

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Let's imagine we've got a
grand father Clock, and the

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length of the pendulum L is
equal to 1 meter.

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So in our formula.

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Going to put 2π multiplied by
the square root L is 1

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meter divided by G is 9.8.

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And that gives us 2π. Now, if
we calculate 1 / 9.8 and then

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square root the answer.

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We get 0.319 *
2 and by pie

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and we end up
with two .007.

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So the period of the pendulum to
the nearest second is T equals 2

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seconds because we've used the
units of meters per second

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squared and meters.

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That was a selection of standard
formerly now for the magicians

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memory trick. I've got a
selection of 30 or so cards

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here, each with eight digit
numbers on, and if I could have

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a helper to select one at random

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for me. Now, if you could
give me the two digit card

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number which is on the top
left hand corner, I'll tell

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you the 8 digit number on
the card number 14 #14.

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OK, the
8 digit

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number is

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314-5943. 7, is that
right? That's correct, very

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good. OK would like to try
another one, just to show that

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it's not a fluke. Can you give
me the two digit number again

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#13 #13? So the 8 digit number

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is 29101. 123, is that correct?
That's correct, good thank you

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very much. Well, I haven't
actually memorized all 30

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numbers that are here. I'm using
a formula, so let's have a look

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now at the numbers and show you
what I did.

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Now the only information I was
given was the card number. This

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number at the top left hand

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corner. So I had to work out the
8 digit number from that card

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number. Now the formula I
was using was 2 N at

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three. What end represents
my card number?

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So for example, the number 10 if
N is equal to 10.

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Then I would do 2 times by 10 at
three, which gives Me 2 * 10 is

00:18:30.089 --> 00:18:36.494
20 at 323, so that gives me my
first 2 digits of the number two

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and three, and then what I do is
add the two digits to get the

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third number. SO2AD3 gives me 5.

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Then the next number comes from
adding the previous 2 digits.

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Three at 5 gives me 8.

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Five at 8 gives me 13, so I'm
going to take the 10 away and

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just write down the three.

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8 at three gives me 11. Again,
I'm going to take the 10 away.

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And write down the one three add
one gives me four and one add 4

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gives me 5, so there's my 8
digit number and all this I was

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given was the card number.

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OK, let's show you another one.
Let's take this one an is 6.

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So 6 is going into my formula to
workout the first 2 digits, so 2

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* 6 + 3 two 6 is a 12
add. Three gives me 15, so the

00:19:40.766 --> 00:19:46.730
first 2 digits are one and five.
Then I add one and five that

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gives me 6 for the 3rd digit I
add five and six. That gives me

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11. I take away the 10 and one
is the next digit.

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Six at one.

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Gives Me 7 for the next one.

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One at 7 gives me 8.

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7 add 8 gives me 15. I take the
10 away, so I write down just

00:20:12.168 --> 00:20:17.390
the Five and eight, add 5 gives
me 13 again. Take the 10 away

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and I end up with three.

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So there we have a magicians
memory trick. Now you can

00:20:24.240 --> 00:20:28.320
obviously make it as easy as
complicated as you like for your

00:20:28.320 --> 00:20:31.380
audience, so you can choose
whatever formula you want.

00:20:32.480 --> 00:20:34.848
And delight your audience.

00:20:36.040 --> 00:20:37.618
So to summarize.

00:20:38.230 --> 00:20:39.859
Working with formerly.

00:20:40.520 --> 00:20:45.070
What you do is substitute
numbers in instead of the

00:20:45.070 --> 00:20:49.620
letters and do the calculation.
But remember the order of

00:20:49.620 --> 00:20:54.170
operations so that you are
correct with your final answer.

00:20:54.920 --> 00:20:55.880
And that's all you do.