Can Shooter

Popping balloons is all well and good, but for added impact the Evil Genius also likes to shoot cans off the wall with his ray gun. Again, there is some deception going on here. The can is a “special” can with some electronics in it. When the beam from the laser hits the phototransistor sensor, a motor swings a weight that hits the side of the can and makes it jump. If the can is carefully balanced, the movement will be enough to make it fall off the surface it is standing on. Figure 5-16 shows the can jumper, which as you might expect just looks like a can full of the Evil Genius’ favorite lunchtime snack. Figure 5-17 shows the schematic diagram for the can jumper. This uses a light sensor in a similar way to the balloon popper. However, in this case, when the laser hits the phototransistor turning on the MOSFET power transistor, rather than heating a

resistor, it turns on a motor that swings an arm around that hits the can. The diode across the motor prevents the high reverse voltages you get when using a motor from destroying the MOSFET

What You Will Need

You will need the components for the can shooter that are listed in the Parts Bin. You do not usually get much information about a small DC motor when buying one. Often, all you get is its nominal voltage. The author found his motor in a local electronics store for a few dollars. You may also find one as part of a scrap toy or an educational motor kit.

Look for a motor about the same size as the one shown in Figure 5-21 later in the chapter. Chances are it should have a similar amount of power. A  4 6V motor should be fine even though we are going to momentarily power it from 9V. It should not have time to burn out for the small fraction of a second it is on. However, do not be tempted to buy a lower voltage than this because you may well burn it out

The battery is a rechargeable 9V PP3 battery. There are good reasons for using a rechargeable battery here. The motor is likely to draw several amps, the battery will become dead quite quickly, and it is greener and more economical to recharge rather than replace. The expanded packing material is going to be used to diffuse the light from the laser. Look for something that will allow light to pass but diffuse it like frosted glass. We also use this useful material in Chapters 7 and 10, which focus on a laser beam alarm and laser voice transmission. 

All the components, including the motor and battery, are mounted onto a piece of perforated prototyping board. This board is like stripboard, but without the strips of copper. It’s just a board with holes drilled into it at a pitch of 0.1 inches. It provides a useful framework to which the components can be attached. Because the motor swings upward, gravity will take care of returning the arm to its resting position, making it ready for the next shot. The design has a micro-switch at the top of the board so the can is turned on when the lid is put in place. Since the lid also blocks out the light to prevent the can jumper from being activated by ambient light, this works well.

Step 1. Cut the Perforated Board

First, find an empty one-pound (450 g) food can. The type with a ring-pull top is needed since it is structurally stronger after it has been opened and has far fewer sharp edges on which to cut yourself. The exact dimensions of cans vary, so you will need to get the length of the perforated board to make an exact fit with your can. The external dimensions of the Evil Genius’ can were 4(1/4)*3 diameter (108mm with a diameter of 75mm). Cut the perforated board with scissors so it is the right length to fill the can from top to bottom. The width is less critical, meaning the width of  1(15/16)  inches (49mm) shown in Figure 5-19 should be fine unless you have a very unusually shaped can. The board should be a snug fit top to bottom

Step 2. Build the Arm Assembly

Electric motors usually just end in a metal shaft. The way we attach the arm to the shaft is to use a screw terminal block as our arm. We can just pop the shaft into one of the terminal connectors and tighten the screw. The terminal block strips usually come with ten or more connections in a strip. We only need five, but they can be easily cut into a section of five, using a knife. The terminal block is reasonably heavy so as to provide some momentum to be transferred into the

 

can. We help this along with a nail, which will also strike the screw. The whole arrangement is shown in Figure 5-20. One of the nails is going to be bent at right angles about half an inch (12mm) from its end. This will strike the self-tapping screw fitted at the right place on the perforated board. The screw will allow the stop point of the arm to be adjusted so it is past the tipping point and will fall back after the can has been shot. The other terminals of the block can be used to attach more weight to the arm. There is, however, a trade-off between the amount of weight on the arm and how fast it moves. So experiment to see what suits your motor best.

Step 3. Attach the Motor

Attach the arm to the motor and position the motor halfway up the perforated board. You now need to mark where the bent nail will hit the perforated board, because we are going to make a hole there so we can fit the self-tapping screw.

Be careful when drilling the perforated board, because it is easy to break if the drill “digs in” to one of the perforations. Choose a drill bit that is just slightly smaller than the diameter of the self-tapping screw. Once the screw is in place, find just the right place for the motor to fit so the nail hits it dead position, make a note of which terminal on the motor was positive. If it just kind of twitches a bit, then try the battery the other way around. At this point, you can also experiment with different weights on the arm to see what works best for your motor

Step 4. Add the Electronics

We can now fit the components to the perforated board. The component leads are pushed in from the top of the board and connected together on the back of the board using the component leads and wire. Figure 5-23 shows the wiring diagram 

Push all of the components into place and then use Figure 5-23 as a reference to connect up the components. The front of the completed board is shown in Figure 5-24, while Figure 5-25 shows the back of the board. Take particular care to get the phototransistor the correct way around. Check its data sheet, but the longer lead is normally the emitter and the shorter lead the collector. The collector goes to the positive 9V supply. Glue the battery clip perpendicular to the board, as shown in Figure 5-24. When connecting wires to the motor, make sure you connect the positive power supply to the connection you found to be positive in the test at the end of the previous section. We can now test everything before we move onto the final stage of fitting it all into the can. While in the can, the phototransistor will be in very low light, so we need to do this testing in fairly low light to prevent the phototransistor from being turned on all the time. We can also turn the preset variable resistor to its most clockwise position to make the sensor as insensitive as possible. Connect everything up and put the arm in its resting place. If the motor is activated, then disconnect the battery immediately and check everything. Remember, if the motor is left on but is unable to move, it may burn out. Now shine the laser (or any light) onto the phototransistor and the arm should fly up to the top position.

Step 5. Prepare the Can

The first thing we need to do is consume the contents of the can and clean it out thoroughly. If the can contains a food that is not to the liking of the Evil Genius (dog food, for instance), it can be fed to a minion since the Evil Genius believes it’s a crime to waste food. The can should be of the

The balloon popper

In this section, we will describe how to make the balloon-popping part of the project. If you are more interested in shooting cans than in popping balloons, skip this section. The balloon popper (Figure 5-8) is a small box containing a battery, a light sensor, and some other electronics. When light from the ray gun hits the light sensor, it turns on a transistor that allows a large current to flow through a resistor. The resistor is fixed to a terminal block and taped to the balloon. The resistor gets hot enough to burst the balloon after 10 or 15 seconds

The balloon popper has a control knob that sets the sensitivity of the sensor, and a switch that can be set to “live,” “off,” or “test.” When set to “test,” the resistor does not get hot; instead, an LED lights up. This lets you set the correct sensitivity. The electronics for the balloon popper are contained in a plastic box. Most of the components are mounted onto the lid of the box. Figure shows the schematic diagram for the balloon popper 

Step 1. Drill the Front Panel and Mount the Components 

Get all the components together and lay them out next to the box so you can see where everything is going to fit. Then, mark the lid of the box where you need to drill holes for the variable resistor, phototransistor, terminal block, switch, and LED. To fix the terminal block, make two small holes, one for each lead, and then glue the block in place (Figure 5-10)

Fit the switch and variable resistor, tightening their retaining nuts with pliers. Drill a hole into which the LED will snugly fit. If it is a tight fit, it will stay in place, otherwise a drop of glue on the underside of the lid will stop it from moving. When all the parts are attached, it will look like Figure 5-11. Notice the glue around the leads of the phototransistor to hold it in place.

Step 2. Solder the Other

Components There is no circuit board in the balloon popper. Since there are only a few components, we can

simply solder the remaining components to those fixed to the box lid. Use the wiring diagram of Figure 5-12 as a guide. The short lead of the phototransistor is the collector. This lead should be connected to the

switch. When all the components and wires are in  place, you should have something that looks like Figure 5-13.

Step 3. Final Assembly

Inspect everything carefully to ensure no wires are touching. If any wires are very close to each other and may move, wrap insulating tape around them

 Before fitting everything in the box, let’s carry out a basic check on the electronics. Fit the batteries into the battery holder; make sure the switch is in the center “off” position and attach the battery clip. Now move the switch to the “test” position (toward the LED). Next, turn the knob from one end of its travel to the other. You should see the LED turn on at some point. Set the variable resistor so the LED is on, but only just on. Then, move your hand over the phototransistor and the LED should go off. If this does not work, go back and check your wiring, and make doubly sure that the phototransistor is the right way around. Once everything is working, fit it all inside the box and screw down the lid (Figure 5-14)

Testing the Balloon Popper

Before we pop our first balloon, we need to check that the resistor gets hot. To do that, set the switch to “test” and turn the knob until the LED comes on. Flip the switch to “live” and hold your finger close to the resistor (don’t touch it). After a few seconds, you should feel heat coming from it

Immediately set the switch back to “off” and wait for it to cool down. The best way to test the balloon popper is to select the nerviest of your minions and have them stand next to the balloon popper to confirm the balloon has popped. First attach the balloon to the resistor using Scotch tape, as shown in Figure 5-15

Set the switch to “test” (toward the LED) and then adjust the variable resistor until the LED is just off, then turn it a little bit further so it is still off. This is adjusting the sensitivity of the sensor so it is not affected by the ambient light. Now shine the ray gun at the balloon. When it comes within a certain range of the phototransistor, the LED should light. Practice aiming the laser at a point where the LED will light, since you will need to keep the beam on this point for ten seconds or so to pop the balloon. When you are confident you can do this, position your minion next to the balloon (as an observer) and then flip the switch to “live.” Aim the beam at the balloon. After ten seconds or so, there should be a loud bang and a terrified minion. You should then repeat the experiment from various distances. Resist the temptation to place the balloon popper on the head of the minion, as you may end up lasering the minion’s eyes

How to make Balloon-popping Laser

The balloon popper is very similar, but this time the transistor passes a large current through a small resistor, heating it up until it is hot enough to pop the balloon attached to it. The power flowing through the resistor is likely to eventually destroy it. Fortunately, the resistors are cheap and for this project can be considered disposable


What You Will Need

You can buy laser modules from standard component suppliers like Farnell and RS, but they tend to be very expensive. So look online, where they should cost no more than two or three dollars. You’ll need the parts shown in the Parts Bin.

Assembling the Gun

The first thing to say about the gun is that you don’t actually have to make it. You could just use a ready made laser pointer. Laser pointers do not look very gun-like, so as an alternative to this design you could modify a pointer by adding a handle and trigger. The gun (Figure) is deliberately made as small and unimpressive as possible to increase the impact of its balloon-popping and can-jumping capabilities. Figure shows the schematic diagrams for the gun. It has only a few

components and they can easily be soldered together without the need for a circuit board. The components are mounted inside a u-section aluminum strip. Lengths of this can be obtained from hardware stores. The components could just as easily have been used on a strip of plastic or even built into a toy gun. The battery clip terminals fit through holes made in the aluminum so that when a PP3 battery is attached, it forms the handle of the gun. The resistor limits the current to the laser diode module. Resist the temptation to buy just a laser diode; instead, look for a laser diode module. The difference is that the “laser diode” will not have a lens, so you will not get the tight beam of a laser

Step 1. Drill the Aluminum Chassis

The u-section aluminum that the author used is shown drilled and filed in Figure 5-4. Be careful to make the holes for the battery clip big enough to ensure that they will not make contact with the aluminum and cause a short circuit. Lay out the components as they will fit onto the chassis and mark with a pencil where you need to drill. You will need a drill bit that’s the correct diameter for the toggle switch and a larger bit to make the holes for the battery clip. After drilling, file off any burrs in the aluminum and file the holes drilled for the battery clip into a square so the clips can fit in place without the contacts touching the aluminum. Try it on for size (Figure 5-5)

Step 2. Solder Everything Up

It is easiest to solder together all the components before fitting them into place. It also means that you can check that it works okay before you glue everything down. Using the wiring diagram of Figure 5-6 as a guide, shorten the leads of the laser module, battery clip, and resistor to the right lengths. Strip the ends of the insulated wires and solder the components together as per the wiring diagram. After everything is connected up, try operating the switch to make sure the laser lights up before moving on to the next step

Step 3. Final Assembly

Fit the retaining screw over the switch and tighten it with pliers. Then, using either epoxy resin glue or a hot glue gun, glue the laser module and battery clip into place. Figure 5-7 shows the parts soldered and glued into place. Testing the Ray Gun The Evil Genius likes to test laser guns with the aid of a pet. Shine the laser in front of your pet (avoid the eyes) and watch them try to catch the red spot on the floor or on the walls

Cats are much better for testing than dogs, because most dogs will abandon the chase once they have worked out that they cannot eat the little red dot. Cats, on the other hand, will happily chase the elusive dot around the room for some considerable time. In this respect, they are somewhat similar to minions

ETAPE 2

How to make a Mini Laser Turret

The turret gun is made of two miniature servos, of the type used in remote control planes, mounted
at right angles to each other so that one sweeps left to right and the other raises or lowers the laser
module. Wires connect the turret to a control unit with a homemade joystick that allows the laser to
be aimed remotely. This project can also be combined with the project in the next chapter to allow the popping of balloons or the jumping of a can by the laser

What You Will Need

To build this project, you will need the components shown in the Parts Bin on the next
page. You can buy laser modules from standard component suppliers like Farnell and RS, but they
tend to be very expensive. So look online, where they should cost no more than two or three dollars. The same applies to the servo motors, and if you are happy to wait a week or two for your parts to
come from China, there are some bargains to be had this way, too

Assembly

The following step-by-step instructions walk you through making the laser turret. First, we construct

the joystick, then the laser and servo assembly, and then the electronics that link it all together.

Step 1. Make a Frame for the Joystick

The construction of the joystick is shown in Figure 4-3. The two variable resistors are fixed to each
other at the flat part of the stems by drilling a

small hole through them and then fixing a nut and bolt through the two. The handle is cut from the
same plastic, a hole drilled in it, and then mounted on one of the variable resistors.
The frame for the joystick is made from a right-angle plastic molding, cut to shape with scissors (Figure 4-4). Any suitable plastic of reasonable thickness is fine for this. The handle for the joystick is made from the same material (Figure 4-5). Both pieces are drilled to fit the variable resistor.

Step 2. Fix the Variable Resistors

Together After cutting and drilling the plastic for the frame and handle, fit the variable resistors and then join
them together through the drilled holes (Figure 4-6).

Step 3. Finish the Joystick

Solder 4-inch (100mm) leads to the center and right connections (looking from the back of the
variable resistor) of each variable resistor. These will be attached to the stripboard when we have
completed it

Step 4. Fix the Laser and Servos

Figure 4-7 shows the design and wiring of the turret module. The laser module is mounted onto

one of the servos. This servo is then mounted onto the arm of the other servo so the bottom servo will control the vertical angle of the laser, and the top servo the horizontal angle. The servos are usually supplied with a range  of “arms” that push onto a cogged drive and are secured by a retaining screw. One of the servos  is glued onto one of these “arms” (Figure 4-8). Then, the arm is attached to the servo. Do not fit the retaining screw yet, since you will need to adjust the angle. Glue the laser diode to a second “arm” and attach that to the servo. It is a good idea to fix some of the wire from the laser to the arm in order to prevent any strain on the wire where it emerges from the laser. You can do this by putting a loop of solid core wire through two holes in the server arm and twisting it around the lead (again, see Figure 4-8).

Next, cut a slot in the can lid so the servo arm can move (Figure 4-8). Afterward, glue the bottom

servo to the lid. Make sure you understand how the servo will move before you glue it.

Once you are sure everything is in the right place, fit the retaining screws onto the servo arms. You may need to adjust these once you come to test the project.

Step 5. Wire the Servos and Laser

The wires from the servos and the laser module will all be connected up to a terminal block

(Figure 4-9). You will need to shorten the leads, and it is much easier to fit them into the terminal

blocks if you solder the leads together first. The colors of the leads on the servo vary among

manufacturers. The leads on the author’s servos were brown for GND, red for +V, and orange for
the control signal. Check the datasheet for your servos to make sure you have the right leads.

Using Figure 4-7 as a reference, wire up the turret. All the negative leads from both servos and the laser module go into the left-hand terminal block. The next terminal block has the positive leads of

the servos and the 100 resistor. The resistor leads should be shortened and the positive lead of the laser module connected to the end of the resistor. The final two connections for the terminal block

are the control signals from the servos. Figure 4-10 shows the completed laser turret module, with the ribbon cable attached and ready to be connected to the stripboard.

Step 6. Prepare the Stripboard

Figure 4-11 shows the stripboard layout for the project. Note that it is shown as viewed from above. Begin by cutting the stripboard to size: we need 15 strips, each with 20 holes. A strong pair of scissors can do this just fine. Using a drill bit, and twisting it between your fingers, cut the track in the locations marked with an “X.” Figure 4-12 shows the back of the board, ready for soldering.

Step 7. Solder the Components

First solder in the linking wires. Use solid core wire, either by stripping normal insulated wire, or by using previously snipped component leads. When all the linking wires are in place, the top of

the board should look like Figure 4-13, and the bottom of the board like Figure 4-14. The trick with the stripboard is to solder the components that rise least from the board first.

That way, when you put the board on its back, they are held in place by the board while you solder them. This being the case, we are going to solder the resistors next. Figure 4-15 shows the board with the resistors in place. We can now solder the timer chip. You may choose to use an IC socket rather than solder the chip directly onto the board. If you do decide to solder the chip directly, be very careful to put it the right way around and in the right place. Once

soldered into place, it is very hard to remove the chip. Also, be careful not to overheat the chip while soldering. Try to do it quickly, pausing a few seconds after soldering each pin. After the chip (or socket), solder the small capacitors (C2 and C4) and the transistor. Again, check that the transistors are the right way around.

Finally, we can solder the large capacitors (C1 and C3) into place, making sure the polarity is correct.
The negative lead is the shorter of the two leads and often has a diamond next to it. The completed board is shown in Figures 4-16 and 4-17.

Step 8. Wire Everything Together

Having built the turret module joystick and stripboard, it is now time to wire everything together. Figure 4-18 shows the wiring diagram  of the project. Using Figure 4-18 as a guide, wire together all the components. The ribbon cable to the servo module is fine for a length of a few feet, but you may run into trouble if you try and attach a long cable. Eventually, the pulse width signal will

become distorted and the servos will behave unpredictably. Alternatively, to get a longer range

with your wires, use multi-core shielded cable, where each of the control signals is in its own screened cable.

So, now that everything is connected, perform a final check to make sure there are no bridges of solder on the stripboard and that all the wires are in the right place. Afterward, insert the batteries and turn it on. The servos should “snap” to the position of the joystick. If nothing happens, or only one of the servos works, disconnect immediately and check everything over.

Step 9. Adjust the Servo Arms

At this stage, you will probably need to adjust the position of the servo arms. With the project turned on, set the joystick to its center position. Remove the two server arms and refit them so the servo is pointing the laser straight ahead, both horizontally and vertically

Step 10. Fit the Project into a Box

Because the joystick has quite a wide range, this is a difficult project to box. However, fitting the battery, the stripboard, switch, and joystick into a box without a lid will at least neaten up the project and provide a firm base for the joystick (Figure 4-19). A hole is drilled for the switch, and another for the cable to the servo turret. The joystick frame is glued to one side of the box. The adventurous Evil Genius may even decide to provide a lid for the box. Ideas The Evil Genius might like to make more than one turret connected to the same joystick. That way, when the joystick is moved, all the turrets move. This is very easy to do. Each turret servo assembly is essentially connected in parallel, as shown Figure 4-20. Theory When it comes to making things move, servo motors are great. They are easy to use, quite low power, and only require one wire to control their position. In this section we learn a little more about how to use Servo motors. We also take a look at the 555 timer IC, which is used to generate the pulses for the project. This timer chip is extremely versatile and it is useful to know how to use it. Servo Motors Servo motors are most commonly used in radio-controlled model vehicles.

Unlike standard motors, a servo module does not rotate around and around. It can only travel through about 180 degrees. The modules are controlled by pulses of voltage on the control connection to the servo. The length of the pulse controls the angle to which the servo is set. Figure 4-21 shows an example waveform. You can see how the width of the pulses varies the servo angle

A pulse of 1.5 milliseconds sets the servo to its center position, a shorter pulse of 1.25 milliseconds to its leftmost position, and 1.75 to its rightmost position.The servo motor expects there to be a pulse at least every 20 milliseconds for the servo to hold its position

The 555 and 556 Timer ICs To generate the pulses for our servo, we use a timer chip. Actually, the chip contains two timers in one package. That is, one for each servo. The chip is an NE556, which contains the

equivalent of two NE555 chips, one of the best-selling chips ever created. This chip has been around since 1971 and sells around a billion units a year. It can be used as both a one-shot monostable that produces just a single pulse, or as an astable oscillator that produces a stream of pulses.

We use it in this astable mode. The overall frequency and duration of the pulses are controlled by the timing components, comprised of a capacitor and two resistors. Figure 4-22 shows the basic arrangement on which our design is based. Using this arrangement, as we said before, the circuit will oscillate, producing a waveform similar to that shown in Figure 4-23

The “high period” shown in Figure 4-23 can be calculated using the formula: 0.69 * (R1 R2) * C where R is in , and C is in F. A 1F capacitor is actually a huge capacitance. Capacitance values are usually measured in μF (microfarads) or even smaller units. The “low period” shown in Figure 4-23 uses the formula:
0.69 * R2 * C Notice that the low period only depends on the value of R2; R1 has no effect on it. This means that we can change the value of R2 to vary the length of the pulse. In our circuit, we use a combination of a variable resistor and a fixed resistor as an equivalent to R2, the total resistance being the sum of the variable resistor and the fixed resistor. The overall frequency will vary, but for servo motors, it’s the length of the pulses that matter, not the overall frequency

This system has one snag: We can easily vary the low period, but the servo motor is controlled  by the high period. This is why we use a transistor connected to the output signal. This transistor inverts the signal, converting the high into low, and vice versa.

Summary

In this project, we learned how to make a joystick from a pair of variable resistors, as well as how to use servo motors. We also explored the extremely versatile 555 timer IC. As an alternative to controlling the servos using a joystick, we could also control them with an Arduino interface board. We will use these small microcontroller boards in Chapters 8, 13, and 15. If you are interested in computerizing your servos and laser, there is a design in the book 30 Arduino Projects for the Evil Geniusby this author (Simon Monk) that does exactly that 

As the convergence of voice and data continues, a more discreet change is also coming  into play. While data is considered fixed to a location, the end user is now more mobile. This opens a new set of challenges for the industry and manufacturers alike, because of  the need for mobility. What once was a simple procedure of connecting the user’s modem to a land line now poses the need to connect that same user to a device while mobile. Protocols need to be more flexible, accommodating the mobile user as the device is  moved from location to location. Moreover, the physical devices (for example, the modems) must be moved often. In a dial-up, circuit-switched communications  arrangement, this is not a major problem. The user can unplug a modem, reconnect it to a landline elsewhere, and dial from anywhere.

However, when we use IP as our network protocol, data is routed based on a network/subnetwork address. Routing tables keep track of where the user is located and route the datagrams (packets) to that subnetwork (see Figure 23-1). When a mobile user logs on and attempts to dial in to the network, the IP address is checked against a routing table and routed accordingly. Updating the tables can be extremely overhead intensive, and it can produce significant amounts of latency in the Internet or Intranet. Using an  ICMP Route Discovery Protocol(IRDP), which is part of the TCP/IP protocol suite,helps. However, when the IRDP process updates its tables, we use a lot of bandwidth. Figure 23-2is an example of the IRDP process where a message is generated by a host to learn all routes available to get to and through the network.

Something needs to be done to accommodate the use of mobile IP by an escalating number of users wanting to log on anywhere. Of course one solution is to use the Dynamic Host Configuration Protocol(DHCP), which uses a server-based mechanism to allocate a new IP every time a user logs onto the network or assigns a static IP address to a user who may be using a diskless PC. The purpose of the DHCP was to facilitate the mobile or not permanently attached user in an ISP network where addresses are limited and casual users are the norm. So the industry had to arrive at a solution allowing casual and nomadic users the same access while they travel (roam) as when they are in there fixed office location. Figure 23-3shows the growth curve of wireless data users attempting to use mobile IP and wireless data communications over the past couple of years. In this graph we see that the numbers justify the concern and the effort being afforded to the problem. The number of wireless users in the world is escalating and the 500 million users shown in this graph are conservative estimates. We are living in a mobile society where users want their data, when they want it, where they want it, and how they want it! What percentage of these wireless users will want data over their connection remains to be seen. However, early estimates are that over one-fifth will want their data in a mobile environment

Le système de coordonnées polaires

Il existe d’autres systèmes permettant de positionner un point dans le repère d’étude comme par exemple le système de coordonnées polaires utilisé dans le cas où le point Mest mobile dans un plan. Le point M  est parfaitement repéré si on connaît la distance OM= ρ et l’angle θ que fait le segment OM avec l’axe Ox (voir figure)

➤Le point origine O correspond au « pôle » d’où le terme coordonné polaire. La longueur du segment OM correspond à sa coordonnée radiale. Elle est notée ρ(rhô : lettre grecque) ou r.

➤L’autre coordonnée est la  coordonnée angulaireégalement appelée angle polaire ou azimut et noté θ (thêta : lettre grecque). Cet angle est mesuré par rapport à l’axe des abscisses Oxappelé alors axe polaire

LES REPÈRES

L’étude cinématique du mouvement d’un point revient à pouvoir répondre aux questions « où ? » (où se trouve le point ?) et « quand ? » (à quel moment dans le temps ?). Pour répondre à ces questions il est nécessaire de définir un repère d’espace et un repère de temps.

a) Repère d’espace

Un repère d’espace est défini par une origine O qui est fixe dans le référentiel et des axes de référence orthonormés c’est-à-dire orthogonaux et munis d’une unité de longueur (vecteur unitaire de norme égale à 1) qui vont permettre à l’observateur de juger dans quelle direction se trouve le point. Les trois axes forment un trièdre direct (voir figure)

L’étude du mouvement dans un plan nécessite 2 axes (Ox, Oy) et dans l’espace 3 axes (Ox, Oy, Oz). À chacun de ces axes est associé un vecteur unitaire respectivement Ux,Uy et Uz . Les vecteurs (Ux,Uy, Uz) forment une base orthonormée.

b) Repère de temps

Pour pouvoir répondre à la question « quand? » il faut ajouter un repère de temps c’est-à-dire une grandeur qui est la variable de temps. La durée écoulée entre 2 événements ou 2 instants est mesurée au moyen d’une horloge ou chronomètre. Tout mouvement périodique (mouvement qui se reproduit identiquement à lui-même à intervalle de temps successifs et égaux pris comme unité de temps) peut servir d’horloge. Le repère de temps est constitué d’une origine des temps fixée par l’observateur et d’une durée unitaire fixant une chronologie. À chaque instant, on associe un nombre réel t appelé date qui correspond à la durée écoulée depuis l’instant origine

En mécanique classique ou newtonienne, on postule que le repère de temps est le même pour tous les référentiels et que le temps s’écoule de la même manière dans des référentiels en mouvement les uns par rapport aux autres

c) Le système de coordonnées cartésiennes

Dans le repère d’espace (O, x, y, z) défini précédemment (voir figure 1.3), un point M est repéré par ses coordonnées d’espace (x, y,z) correspondant à la mesure algébrique de la projection de M successivement sur les 3 axes du repère. Ces 3 coordonnées sont de même nature et homogènes à une longueur. Dans le référentiel R d’étude, la base associée à ce système d’axe (Ux,Uy,Uz) est une base orthonormée qui ne change pas au cours du temps. On dit encore que la base est fixe dans R