A moment is the turning effect of a force.
Moment (Nm) = Force (N) * perpendicular distance (m) between line of action and pivot
The centre of mass falls directly below the line of suspension. The find this in a symmetrical shape you simply look at where the lines of symmetry intersect.
However, if the object is not symmetrical then you can still find the centre of mass. There are 4 easy steps:
- Hang the shape and a piece of string with a weight on it from the same point
- When they stop moving, draw a line along the piece of string, onto the shape
- Repeat this but from a different point
- Where these lines intersect is the centre of mass
If the clockwise and anticlockwise moments are equal the object will not turn (there is no resultant moment).
If they aren't equal there will be a resultant force. The position of the centre of mass is very important. A low centre of mass will make an object more stable. A wide bas will also make it more stable because the line of action will remain within the base. The line of action is an imaginary line that runs from the centre of mass, perpendicular to the ground. If it falls outside the base then the object is likely to topple over due to a resultant moment.
Take a ruler and balance it on your finger. Now take two light objects and place them on either end of the ruler. Try to balance it again. What do you notice about the position fo your finger, with and without the objects?
The velocity of an object travelling in a circle is always changing. This is because velocity takes into account the direction as well as the speed. The direction is always changing so the velocity is always changing. This also means that it is accelerating because it is contstantly changing direction. It accelerates towards the centre of the circle. A force must be acting on it to make this happen and this force is called centripetal force. It can be caused by 3 forces:
- friction - e.g. a car going round a corner
- tension - e.g. a bucket on a rope
- gravity - e.g. planets in orbit
Centripetal force depends on mass, speed and radius.
- the faster an object is moving, the bigger the centripetal force needed
- the heavier the object, the bigger the centripetal force needed
- the smaller the circle, the bigger the centripetal force needed
Gravity and Planets
Gravity is the force of attraction between masses and the larger the mass the greater the force of gravity. It is what keeps us on Earth.
It is also the centripetal force that keeps planets in orbit. An orbit is possible when the forward motion of the object and the gravitiational force pulling it inwards are balanced.
Planets always orbit around stars like Earth orbitting the Sun. The centripetal force is the gravity between the Sun and Earth. These orbits are slightly elliptical with the Sun at one focus of the ellipse. The greater the distance from the planet to the Sun, the longer the orbit.
Gravity decreases as you get further away (because the centripetal force does) meaning that the closer the planet is to the Sun, the greater the gravitational pull. This means that planets must travel faster to counteract the strong pull of gravity and so cover their orbit quicker.
So Uranus has a weaker gravitational force, a bigger orbit, travels slower and takes longer to complete it's orbit than Earth.
Mercury has a stronger gravitational force, a smaller orbit, travels faster and completes it's orbit quicker than Earth.
Satellites are also held in orbit by gravity as are comets.
A satellite can be natural or artificial. Natural satellites are moons and there are two main types of artificial satellite.
Geostationary Satellite - These have high orbits over the equator and take exactly 24 hours to complete their orbit meaning that they remain in the same place over the Earth's surface because the Earth rotates with them. This makes them very good for communications such as telephones and TV signals.
Low Polar Orbit Satellite - These have low orbits and sweep over both poles in a few hours. The Earth rotates beneath them and so they can cover the whole surface of the Earth each day. They are good for weather reports and spying on other countries.
A real image is formed at the intersection of real rays and a virtual image is formed where the rays appear to come from (so where virtual rays intersect).
When you look in a mirror you get a virtual image because the object appears behind the mirror. A magnifying lens also creates a virtual image because it looks bigger and further away than it actually is.
When describing an image you must describe the size, whether it's upright or upside down and whether it's real or virtual.
Reflection of light helps us see things because light bounces off of surfaces and into our eyes. Smooth surfaces have a clear reflection because all light rays are reflected at the same angle where as rough surfaces (such as a piece of paper) reflect light at lots of different angles so a diffuse reflection is formed.
Angle of incidence = angle of reflection
These angles are between the normal the the ray. The normal is an imaginary line that's at right angles to the surface.
Refraction is the bending of light as it enters a different medium. It happens because the rays change speed.
Plane mirrors - The image is the same size as the object. It is as far behind the mirror as the object is in front and it is formed from diverging rays so is a virtual image.
To draw a ray diagram for a plane mirror you must first draw the image, remembering the rules above. Then draw a reflected ray from the top of the image to the top of the eye. Remember that it should be a dotted line behind the mirror. Then draw a ray from the top of the object to where the reflected ray hits the mirror. Repeat for the bottom of the eye.
Curved mirrors - These are a bit different. You can have concave mirrors, which are shiny on the inside of the curve and converge light rays and you can have convex mirror, which are shiny on the outside of the curve and diverge light rays. A vertex is right in the middle of the mirror's surface. An axis then runs from this point outwards, perpendicular to the mirror. On this line are focal points (F, C and 2F) which will be drawn for you in the exam.
Ray Diagrams - Mirrors
These need practise. However there are 4 rules you need to remember to make drawing these easier.
- Decide if the mirror is converging or diverging. (converging = concave like a spoon.)
- Draw an incident ray running parallel to the axis and reflect it so that it will pass through F.
- Draw an incident ray that runs through F (or appears to pass through F if it is a convex mirror) and reflect it parallel to the axis.
- Draw a ray passing straight through 2F/C (or appears to pass through this point) and reflect it straight back on itself.
Now find where your 3 reflected rays intersect. If they don't seem to intersect then extend them back on themselves using dotted lines and they should intersect. This is where your image is and it drawn with the base of the object on the axis and the top touching the intersection, even if the intersection is below the line.
Now describe your image as we have learnt before. Convex mirrors are always virtual, upright, smaller than the object and behind the mirror whereas concave mirrors change.
Remember to use dotted lines when the rays pass behind the mirror.
Lenses change the direction of light rays by refraction. The ray bends towards the normal as it enters the denser medium and away from the normal as it goes into the less dense medium. White light can be split by passing through a triangular prism if the angle is correct.
Different lenses produce different kinds of image. A converging lens bulges outwards and is convex. The light rays meet at a certain point called a focus. This lens is what is in our eyes and focusses the light rays on the retina. A diverging lens caves inwards and is concave. It causes the light rays to diverge as though they all came from the same point.
There is still an axis, focal points and a vertex, just like mirrors. Each lens has a focal point in front of the lens and one behind that are the same distance from the mirror.
Ray Diagrams - Lenses
Again there are a number of rules to learn for lenses:
- Is it diverging or converging? (if it bulges outwards the rays come inwards)
- Draw an incident ray parallel to the axis that passes through the focal point (convex - on the other side of the lens, concave - it appears to come form the focal point)
- Draw an incident ray passing through/towards the focal point and refract it so that it goes parallel
- Draw an incident ray passing straight through the vertex with no refraction
Now draw your image where the refracted rays intersect or extend the lines backwards using dotted lines to find where they intersect.
You can now describe your image. A concave lens always produces a virtual, upright image that is smaller than the object and on the same side of the lens as the object.
Remember that light refracts not reflects with lens. Dotted lines should be used when the rays appear to come from somewhere.
Uses of lenses
Magnifying glasses use convex lenses because they produce a virtual image that is closer to the lens that the object (as long as the object is closer than F).
Sometimes you have to work out the magnification of an image. The formula for this is really simple:
magnification = image height / object height
If they give you squared paper then you can just count the squares, if not you can just measure it with a ruler.
Taking a photo forms an image on to film (or sensor if a digital camera). The image must be real because you can't project a virtual image onto a screen and the light rays actually meet there. The image is also smaller than the object because it's a lot further away than the focal length of the lens. The image is inverted. A camera uses a convex lens, just like a magnifying glass and our eyes.
Sound travels as waves which are caused by vibrating objects. These vibrations are passed through the surrounding medium and are known as longitudinal waves. Sometimes the sound will eventually reach someone's eardrum which is when they hear it. The denser the medium, the faster sound travels through it. Sound travels further in solids than in liquids and faster in liquids than gases.
Sound waves can reflect and refract. They are reflected by hard, flat surfaces ( things like carpets absorb sound). They will also refract as they pass through different media. As they enter the denser material, they speed up.
Humans hear in the frequency range of 20 - 20,000Hz which is the number of waves a second.
Sound doesn't travel in a vacuum because there aren't any particles to travel through.
Sound Waves (continued)
Loudness increases with amplitude which is the height from the middle of the wave to the top of a peak.
The higher the frequency, the higher the pitch. Frequency is the number of waves per second.
Different shaped waves give different types of sound. For example, a waveform of rectangular peaks creates and thin and reedy sound, like an oboe.
Watch the above video. Why does this happen?
Ultrasound is a sound with a higher frequency than we can hear. It is above 20,000Hz. Ultrasound waves get partially reflected at a boundary between media. Some is transmitted and refracted but some reflects back and this normally goes to a detector. This can measure how far away the boundary is.
An oscilloscope trace (CRO trace) can be used to find boundaries. Given the seconds per division setting of the CRO you can work out the time between pulsed by measuring on the screen. Then, if you have the speed of sound in the given medium then you can work out the distance using the speed = distance / time formula. Or they might give you the frequency and the wavelength so you can work out the speed of the wave from this and then use the other equation.
There are a number of uses:
- cleaning - very high frequency vibrations break up the dirt into small particles that fall off. This method is very delicate so the mechanisms/teeth/jewellery could get damaged
- industry quality control - can find cracks in metal casting etc.
- pre-natal scanning of a foetus - hits boundaries between amniotic fluid (what the baby is in) and the baby
Bats use a similar method to "see" with. They send out ultrasonic squeaks which reflect off things and they can work out how far away the object is.
A magnetic field is a region where magnetic materials and wires carrying currents experience a force acting on them. The arrows on the field lines always point from the north pole of the magnet to the south pole. The magnetic field round a straight, current-carrying wire is made up of concentric circles.
The right hand thumb rule. You're thumb points in the direction of current and your fingers wrap around in the direction of the magnetic field.
The magnetic field round a solenoid. The magnetic field inside a solenoid is strong and uniform. Outside the coil the magnetic field is just like one around a magnet. The ends of a solenoid act like north and south poles. If the direction of the current swaps, so does the north and south poles. A magnetically soft material (such as iron) magnetises and demagnetises very easily. As soon as you turn the current off, the magnetic field disappears.
The Motor Effect
A current in a magnetic field experiences a force. Placing a wire in a magnetic field will cause it to move due to a force acting on it, as long as the wire is placed at 90 degrees to the field.
Fleming's left hand rule tells you which way the force acts. Using your left hand, point your First finger in the direction of the Field and your seCond finger in the direction of the Current. Your thuMb shows the direction of the force/Motion.
The simple electric motor has 4 factors which speed it up: more current, more turns on the coil, stronger magnetic field, soft iron core.
The split-ring commutator swaps the contacts every half turn to keep the motor rotating in the same direction. The direction of the motor can be reversed either by swapping the polarity of the DC supply or swapping the magnetic poles over.
Electromagnetic induction is the creation of voltage (and maybe current) in a wire which is experiencing a change in magnetic field. You can do this be moving a magnet in a coil of wire or moving a conductor in a magnetic field (cutting through the field).
If you move the magnet or change the polarity of the magnet in the opposite direction then the voltage is reversed too. If you keep the magnet moving backwards and forwards you'll produce AC current.
You can create the same effect by turning a magnet end to end in a coil. This is how generators work. As you turn the magnet, the magnetic field through the coil changes and induces an AC voltage, which in turn can create AC current.
Four things affect the size:
- strength of magnet
- number of turns on coil
- area of the coil
- speed of the movement
Generators rotate a coil in a magnetic field and look a bit like a motor. The current is induced and changes every half turn. Slip rings and brushes are used so the contacts don't swap every half turn. This means AC voltage is produced.
Dynamos are like this but you turn the magnet instead of the coil. They work in exactly the same way but it is the magnet that is turning instead. They are often used on bikes to power the lights and use a cog wheel that is turned by one of the bike wheels.
These generators and motors are all very similar and can get very confusing. Split a piece of paper in half and summarise everything we have learnt in the last few slides. Try and do it without looking back at them but do check that you have got it all correct.
Theses change AC voltage by producing an alternating magnetic field. The iron core magnifies this so that it covers the secondary coil as well as the primary coil. This alternating field then induces an alternating voltage in the secondary coil which in turn creates AC current. Step-up transformers have more turns on the secondary coil than the primary coil and step-down transformers have less. They are used all over the National Grid because wires carry power with very high voltages and keep the current low (to save on power loss due to resistance). This means that you need step-up transformers to step up the power before it enters the wires, and then a step-down transformer at the other end.
There is an important equation that can be used to calculate the number of coils on the primary or secondary coil or either the primary or secondary voltage.
primary voltage/secondary voltage = number of turns on primary/number of turns on secondary
Simply substitute the figures you know and solve!
Stars and Galaxies
Stars and solar systems form from clouds of gas and dust. Gravity compresses the matter so much that intense heat develops and sets off nuclear fusion reactions. This causes light to be emitted. The left over lumps spiral around the star and form planets.
The early universe only contained hydrogen. Directly after the big bang, only hydrogen existed. This was converted into helium via nuclear fusion. Once the hydrogen runs out, helium fuses to form carbon which fuse to form heavier elements such as oxygen and helium. When the helium runs out, the carbon, helium and hydrogen fuse to make silicon. This keeps happening until iron is formed. When stars explode (At the end of their life) all elements are formed and then scattered across the universe.
The Life Cycle of a Star
Clouds of dust and gas ---> Protostar ---> main sequence star ---> red giant
then small stars form ---> white dwarf ---> black dwarf
large stars form ---> a supernova and then either a new planetary nebula and new solar system or a neutron star followed by a black hole.
- stars initially form from clouds of dust and gas
- the force of gravity pulls these into a protostar
- high temperatures cause nuclear fusion to occur, making a main sequence star
- eventually the hydrogen runs out an a red giant forms
- a small star cools and contracts into a white dwarf and then a black dwarf when the light fades
- big stars glow brightly, undergo more fusion and then explode in a supernova
- this throws dust and gas into space leaving a dense core called a neutron star or a big hole
- the dust and gas can form second generation stars with heavier elements