# simplified general physics notes

General Physics

Length and Time

LENGTH

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A rule (ruler) is used to measure length for distances between 1mm and 1meter.

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For even smaller lengths, use a micrometer screw gauge.

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SI unit for length is the meter (m)

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To find out volume of regular object, use mathematical formula

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To find out volume of irregular object, put object into measuring cylinder with water. When

object added, it displaces water, making water level rise. Measure this rise. This is the

volume.

TIME

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Interval of time is measured using clocks or a stopwatch

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SI unit for time is the second(s)

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To find the amount of time it takes a pendulum to make a spin, time ~25 circles and then

divide by the same number as the number of circles.

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Motion

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Speed is the distance an object moves in a time frame. It is measured in meters/second

(m/s) or kilometers/hour (km/h).

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Speed is a scalar quantity as it only shows magnitude.

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Speed in a specified direction is velocity, which is a vector

SPEED TIME GRAPHS

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Area under the line equals to the distance travelled

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Gradient = \frac{y_2 – y_1}{x_2 – x_1} = \ \frac{\mathrm{\Delta}v}{t}Gradient=x2−x1y2−y1

= tΔv = Acceleration (m/s)2

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Positive acceleration means the velocity of a body is increasing

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Deceleration or negative acceleration means the velocity of a body is decreasing

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A curved speed time graph means changing acceleration.

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Acceleration is the rate of change in velocity per unit of time, and a vector as it’s direction is

specified

DISTANCE TIME GRAPHS

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{Gradient =}\frac{y_2- y_1}{x_2-x_1} = \frac{{\Delta}d}{t} =Gradient=x2−x1y2−y1=tΔd= Speed

(m/s)

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Therefore, distance:

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With constant speed: Speed\ \times \ TimeSpeed × Time

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With constant acceleration1: \frac{Final\ Speed + Initial\ Speed}{2} \times

Time2Final Speed+Initial Speed×Time

ACCELERATION BY GRAVITY

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An object in free-fall near to the Earth has a constant acceleration caused by gravity due to

the Earth’s uniform gravitational field

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Objects are slowed down by air resistance. When deceleration caused by air resistance =

acceleration by gravity, i.e. no net force acting on a body in free fall, the body reached

terminal velocity

Mass and Weight

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Mass: A measure of matter in a body and the body’s resistance to motion.

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Weight is the force of gravity on a body as a result of its mass.

\mathbf{Weight = Mass \times Gravity}Weight=Mass×Gravity

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Weights (and hence masses) may be compared using a balance

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Density

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Density of a liquid: Place measuring cylinder on balance. Add liquid. Reading on measuring

cylinder = V, change in mass on balance = m. Use formula.

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Density of solid:

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Finding the volume: To find out volume of a regular object, use mathematical

formula. To find out volume of an irregular object, put object into a measuring

cylinder with water and the rise of water is the volume of the object.

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Finding the mass: Use balance

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An object will float in a fluid if it’s density is lesser than the density of the liquid, i.e. The

volume of fluid displaced has a greater mass than the object itself.

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Example: an orange with its peel has a density of 0.84g/cm3, we can predict that it will float

in water because it is less than 1 g/cm3 (density of water). We can also say, that an orange

without its peel, which has a density of 1.16g/cm3, will sink because it is greater than

1g/cm3.

Forces

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Force is measured in Newtons

\mathbf{Force = Mass \times Acceleration}Force=Mass×Acceleration

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1 Newton is the amount of force needed to give 1kg an acceleration of 1m/s2

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A force may produce a change in size and shape of a body, give an acceleration or

deceleration or a change in direction depending on the direction of the force.

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The resultant of forces acting in the same dimension will be their sum, provided a

convention for directions is set. Therefore, the resultant of 2 forces acting in the same

dimension, in the opposite direction will be the difference in their magnitude in the direction

of the greatest.

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If there is no resultant force acting on a body, it either remains at rest or continues at

constant speed in a straight line

RESISTIVE FORCES

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Friction: the force between two surfaces which impedes motion and results in heating

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Air resistance is a form of friction

NEWTON’S LAWS OF MOTION

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First law of motion: If no external for is acting on it, an object will, if stationary, remain

stationary, and if moving, keep moving at a steady speed in the same straight line

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Second law of motion: \mathbf{F = ma}F=ma

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Third law of motion: if object A exerts a force on object B, then object B will exert an equal

but opposite force on object A

HOOKE’S LAW

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Springs extend in proportion to load, as long as they are under their proportional limit.

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Limit of proportionality: point at which load and extension are no longer proportional

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Elastic limit: point at which the spring will not return to its original shape after being

stretched

\mathbf{F = kx}F=kx

CIRCULAR MOTION

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An object at steady speed in circular orbit is always accelerating as its direction is changing,

but it gets no closer to the center. The speed of the ball stays constant.

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Centripetal force is the force acting towards the center of a circle. It is a force that is needed,

not caused, by circular motion,

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For example, when you swing a ball on a string round in a circle, the tension of the string is

the centripetal force. If the string is cut then the ball will travel in a straight line at a tangent

to the circle at the point where the string was cut.

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Centrifugal force is the force acting away from the center of a circle. This is what makes a

slingshot go outwards as you spin it. The centrifugal force is the reaction to the centripetal

force. It has the same magnitude but opposite direction to centripetal force.

Moments

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A moment is the measure of the turning effect on a body and is defined as:

\mathbf{\text{Moment}}\left( \mathbf{\text{Nm}} \right)\mathbf{= Force}\left( \mathbf{N}

\right)\mathbf{\times Perpendicular\ distance\ from\ Pivot}\left( \mathbf{m}

\right)Moment(Nm)=Force(N)×Perpendicular distance from Pivot(m)

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Therefore, increasing force or distance from the pivot increases the moment of a force

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This explains why levers are force magnifiers

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Turning a bolt is far easier with a wrench because the perpendicular distance from

pivot is massively increased, and so is the turning effect.

In equilibrium, clockwise moment = anticlockwise moment there is no resultant force acting

on the body.

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This can be proven by hanging masses of the same weight on opposite sides of a

meter rule on a pivot at equal distances from the pivot showing that the meter rule

in stationary.

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Centre of Mass

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Centre of mass: imaginary point in a body where total mass of body seems to be acting.

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An object will be in stable equilibrium when it returns to its original position given a small

displacement.

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For an object that is displaced, it will stabilize only if the force caused by it’s weight is within

it’s base.

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For an object to start rotating it needs to have an unbalanced moment acting on it

Scalars and Vectors

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A scalar is a quantity that only has a magnitude (so it can only be positive) for example

speed.

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A vector quantity has a direction as well as a magnitude, for example velocity, which can be

negative.

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Calculating resultant force:

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A parallelogram has to be made with the acting forces (F1 and F2). The resultant force will be

the diagonal. Make sure the same scale is used to convert between length and forces.

Measure length of diagonal and use scale to convert value into force (FR).

Momentum

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Momentum: product of mass and velocity

\mathbf{p\ = \ mv}p = mv

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Principle of conservation of linear momentum: when bodies in a system interact, total

momentum remains constant provided no external force acts on the system.

\mathbf{m_Au_A+m_Bu_B=m_Av_A+m_Bv_B}mAuA+mBuB=mAvA+mBvB

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Impulse: product of force and time for which it acts

\mathbf{Ft} \ \mathbf{=} \ \mathbf{mv} \ – \mathbf{mu}Ft = mv −mu

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Energy

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Energy: amount of work and its measured in Joules (J)

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An object may have energy due to its motion or its position

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Conservation of energy: energy cannot be created or destroyed, when work is done, energy

is changed from one form to another.

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Energy can be stored

Energy type

What it is

Example

Kinetic

Due to motion

Car moving

Gravitational

From potential to fall

Book on shelf

Chemical

In chemical bonds

Bonds in starch (food)

Strain

Compress/stretch

Stretched elastic band

Nuclear

Atoms rearranged/split

Released in nuclear plant

Internal

Motion of molecules

In a glass of water

Electrical

Carried by electrons

Battery to bulb

Light

Carried in light waves

From sun

Sound

Carried in sound waves

From speaker

Kinetic\ energy = \frac{1}{2} \times Mass \times \text{Velocity}^{2}Kinetic energy=21

×Mass×Velocity2

\mathbf{K.E. =}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}\mathbf{v}^{\mathbf{2}}K.E.=21mv2

Graviational\ Potential\ Energy = Mass \times Gravity \times

HeightGraviational Potential Energy=Mass×Gravity×Height

\mathbf{G.P.E. = mgh}G.P.E.=mgh

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Example of conversion of energy: A book on a shelf has g.p.e , if it falls of the shelf it will

have k.e

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Due to the processes through which energy transfers take place not being 100% efficient,

energy is lost to the surrounding and therefore energy gets more spread out (dissipated)

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Efficiency: how much useful work is done with energy supplied

\mathbf{Efficiency =}\frac{\mathbf{\text{Useful energy output}}}{\mathbf{\text{Energy

input}}}\mathbf{\times 100\%}Efficiency=Energy inputUseful energy output×100%

\mathbf{Efficiency =}\frac{\mathbf{\text{Useful power output}}}{\mathbf{\text{Power

input}}}\mathbf{\times 100\%}Efficiency=Power inputUseful power output×100%

Energy Resources

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Renewable sources are not exhaustible

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Non-renewable sources of energy are exhaustible

Type

Fuel: burnt to make thermal energy, makes

steam, turns turbine

Advantages

Disadvantages

Cheap, Plentiful,

Low-tech

Harmful wastes:

(Greenhouse/

pollutant gas,

Radiation)

Wave energy: generators driven by up and

down motion of waves at sea.

No greenhouse gases

produced

Tidal energy: dam built where river meets

sea, lake fills when tides comes in &

empties when tide goes out; water flow

runs generator

No greenhouse gases

produced

Hydroelectric: river & rain fill up lake

behind dam, water released, turns turbine

∴ generator

Difficult to build

Expensive

Low impact on

environment

Energy produced at

constant rate

Can’t be built

everywhere

Few areas of the

world suitable

Geothermal: water pumped down to hot

rocks rising as steam

No CO2 produced

Deep drilling difficult

and expensive

Nuclear fission: uranium atoms split by

shooting neutrons at them

Produces a lot of

energy with very

little resources

Produces radioactive

waste

Wind: windmills are moved by the breeze.

They generate electricity from kinetic

energy.

No CO2/ Greenhouse

gasses produced

Few areas of the

world suitable.

No CO2 produced

Variable amount of

sunshine in some

countries

Solar cells/ photovoltaic cells: made of

materials that deliver electrical current

when it absorbs light

Type

Advantages

Disadvantages

Solar panels: absorbs energy and use it to

heat water

Work and Power

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Work is done whenever a force makes something move.

W = \ \mathrm{\Delta}EW= ΔE

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The unit for work is the Joule (J).

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1 joule of work = force of 1 Newton moves an object by 1 meter

\mathbf{\text{Work done }}\left( \mathbf{J} \right)\mathbf{= \ \ Force\ (N) \times Distance\

(m)}Work done (J)= Force (N)×Distance (m)

\mathbf{W = FD}W=FD

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Power is the rate of work

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The unit for power is Watts (W)

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1W = 1J/s

\mathbf{Power\ (W) =}\frac{\mathbf{Work\ Done\ (J)}}{\mathbf{Time\ Taken\

(s)}}Power (W)=Time Taken (s)Work Done (J)

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Pressure

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Pressure is the force per unit area.

\mathbf{\text{Pressure }}\left( \mathbf{\text{Pa}} \right)\mathbf{=}\frac{\mathbf{Force\

(N)}}{\mathbf{Area\ (}\mathbf{m}^{\mathbf{2}}\mathbf{)}}Pressure (Pa)=Area (m2)Force (N)

\mathbf{P =}\frac{\mathbf{F}}{\mathbf{A}}P=AF

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Unit: Pascals (Pa) = N/m2

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In Liquids

\mathbf{\text{Pressure}}\left( \mathbf{\text{Pa}} \right)\mathbf{=

Density(kg/}\mathbf{m}^{\mathbf{3}}\mathbf{) \times

Gravity(m/}\mathbf{s}^{\mathbf{2}}\mathbf{) \times

Height(m)}Pressure(Pa)=Density(kg/m3)×Gravity(m/s2)×Height(m)

\mathbf{P = h\rho g}P=hρg

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Therefore, as the depth of a fluid increases, the pressure caused by the whole liquid

increases.

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Measuring Pressure: Manometer

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Measures the pressure difference

•

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The height difference shows the excess pressure in addition to the atmospheric

pressure.

Measuring Pressure: Barometer

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Tube with vacuum at the top and mercury filling the rest.

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Pressure of the air pushes down on reservoir, forcing mercury up the tube.

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Measure height of mercury

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~760 mm of mercury is 1 atm.

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