Circular Motion - GCSE & A-level Physics

you only need one condition to be true in order to something to move in a circle let's say that I'm swinging a clunker around my head and I have my piece of string going towards me in the middle there let's say that the concrete velocity V is going that way as it's in front of me there now I want to change the direction that it's going in I don't want to change its speed at all I just want to change its direction you should remember from Newton's second law that if you have a resultant force you have acceleration as well but acceleration doesn't have to mean change in speed because change in velocity can mean change in speed or change in direction because velocity is made up of both of those the only way that I can apply a force in order to make sure that this concrete doesn't speed up or slow down is towards me I could push out and that would have the same effect but of course I've just got my piece of string here so we're going to forget about that there are at 90 degrees to each other there are right angles to each other let's go a split second into the future and my conker is now here is its velocity going the same way that it was no because I have pulled sideways on it 90 degrees to velocity and I've changed the direction of its velocity it's still going the same speed just in a different direction if I pull with the same force downwards like so now if I pull downwards on this conker now then I'm going to be pulling a little bit in the same direction as the velocity which means it's actually going to speed up that's not what I want to talk again the only thing that I can do is pull 90 degrees to its velocity and this will carry on all the way around until it forms they circle around me so the only condition that you need to circular motion is this force is constantly acting 90 degrees to the object's velocity towards the center of the circle that goes for any sort of circular motion that you have at all that could be a satellite going around the earth where the satellites weight and the force of gravity is actually pulling towards the center of the earth at all times obviously and the car goes around the roundabout the friction between the tires and the road that's also acting towards the center of the roundabout at all times we call this force centripetal force now you might hear we call the centripetal force but hey I'm British I Gordon centripetal force a centripetal force is one that is always acting towards the center of the circle then you might hear centrifugal force centrifugal force is a bit of a weird one it's the sort of fake force that you think you're feeling as you're being pushed out and say if you are a roundabout you feel like you're being pushed out of the car and in fact all you're feeling is the centripetal force pushing you in towards the center of the circle so there's no real such thing as the centrifugal force now there is an equal and opposite reaction force in any situation of course you could call that the centrifugal force but we don't see that the force is always 90 degrees to the velocity so we could say the velocity is always at a tangent or tangential to the objects path in other words it's always out of tangent to the circle we can see that there put a ruler there that's on a tangent touch the velocity and there and there you get the idea what would happen if my string snapped all of a sudden so there's no more tension and it is no more centrifugal force some people think that the clunker would actually fly out in this direction that's not true at all is it because that means that we're creating a velocity out of nowhere the conquer at this point is going this way so if the string snapped right then and I concur with fly off in that direction things always fly off at a tangent if the centripetal force is all of a sudden removed so with a bit of help from planet coaster let's see what this looks like in reality or not quite reality but you get what I mean so we have a thrill ride here and each of these capsules is undergoing circular motion and is constantly accelerating towards the center let's put on the arrow showing the centripetal force for one of these capsules now the centripetal force here would be the tension in the metal bar that is connecting it to the hub we also see this with the chair swing right and the people in their chairs get flying outwards they would go flying off at a tangent but the tension in the wires keeps them accelerating towards the center but not getting any closer that makes them go in a circle now on a loop-the-loop on a roller coaster the centripetal force is the support force exerted on the cars towards the center of the loop using only half a loop we can demonstrate what happens when the centripetal force is suddenly removed the centripetal force is there as it goes round the circle and then at the top the velocity is going to the left and the centripetal force is removed because it runs on a track and therefore it no longer accelerates towards the center and just slide off to the left so that's where the GCSE ends pretty much let's have a look at some a lovely stuff there's our object going in a circle going around this way here and before so as be usual is acting towards the center here there's a selasa T at that point in time there also be a circle that means that the object has to be the same distance away from the center at all times and it's at a distance R that's the radius so we know that it has a speed V it's our away from the center of the circle and we have a force F now we know that the object is constantly accelerating towards the center of the circle because that's the way that the force is pulling that has to be true force is pulling towards if a force is pulling in a certain direction that's the way the acceleration has to be going as well but what's weird is that it's not getting any closer to the center of the circle so a satellite going around the earth is constantly accelerating towards the center of the earth but it's not getting any closer kind of weird the acceleration that something experiences going around in a circle is equals to V squared over R a velocity squared over the units work out we end up with meters per second squared putting this into F equals MA we end up with F equals MV squared over R and that's the main equation that you're going to be using for circular motion now later on in gravitational field and magnetic field and electric field you're going to be equating this force to other forces as well so you're going to be using this equation a lot especially probably in the second year of your anal so this force could be the tension in a string that's making something fly around in a circle or it could be equals to an object's weight if it's going around in an orbit around the Earth or it could be equals to friction or it kids like I said be equals to force due to an electric field or a magnetic field as well what can we do with this then well you're usually given the mass of an object and you're probably given the radius as well we might be asked to figure that out a lot of time you're not given the speed but instead you're given the time that it takes for an object to go around in a full circle we know that a time period is the time it takes for anything to complete a full cycle and we call that T that seconds there's a capital T not little T don't forget as well that frequency is 1 over the time period and vice versa as well so you could be given the frequency and you have to use that instead we'll use this in a second Oh something speed is equals to distance over time the time that we're talking about is the time period here and we have a full circle so what's that going to be 2 pi R over T and using frequency instead we get 2 pi F ah this is where we introduced something new 2 pi F has its own special symbol and that's an Omega soar like a curly Greek w this is called angular velocity or angular speed and we measure it in radians per second why because we have 2 pi that's the amount of radians in a full circle times f which is frequency which is Hertz but that's per seconds as well as to the minus 1 so angular velocity is just telling us how many radians per second an object is doing so we can see that V equals Omega R Omega depend on how you say it Omega is also going to crop up in simple harmonic motion as well so it's worth getting a head around now let's consider a satellite going around the earth a geostationary satellite here's the path that the satellite is taking so if I ask you to draw where the radiuses that you might be tempted to draw on here in our given surface but course with circular motion the radius has to go from the center of the circle so that the center of the earth now what do we know about a satellite that's in a geostationary orbit we know that it's above the same point on the surface and that has to be above the equator obviously because if it's anywhere else it's not going to go in a perfect circle around the Earth so we know that the time period for this to do one complete orbit of the earth is 24 hours because it's following the Earth's rotation times up by 3600 that's the number of seconds in an hour and we get 86,400 seconds the radius of this orbit I can tell you is 4 point 2 times 10 to the 7 meters that's 42 thousand kilometers that's from the centre of the earth and the mass of this satellite is 50 kilograms what if I ask what is the centripetal force felt by this satellite at any given time we know from earlier that F is MV squared over R now we have M we have R we don't have V let's find out V we could do the whole 2 PI R divided by the time period that gives us a speed of 3.0 5 times 10 to 3 meters per second then we could pop that back into there and we could climb to force that way we could do that but you might notice that there is a bit of a shortcut because we know that V here's Omega R we can put that back into here let me actually end up with F equals M Omega squared ah so in fact we do not need to know how fast the satellite is going we don't need to know its actual speed all we need to know is its angular velocity and in order to find that out let's do M 2 PI over T squared times R Omega is 2 pi F that's also the same as 2 pi over the time period so square that this is 50 times 2 pi divided by 8 6400 school weird times the radius which is 4 point 2 times 10 to 7 that gives us a force of 11.1 Newtons that's a big-ass entropy or for that actually is what about if we've got a plane and it's coming towards you and what it's doing is that it's banking in other words it's going in a circle not your ring at all all it's doing is pulling upwards as it were at an angle so it's going in a circle like this and that's the radius of its path as it goes in a circle and we know that if it's pulling up then it must be providing a force in this direction here perpendicular to the wings let's say that we know this angle here to be theta if it's going in a flat circle as well we also know that whatever component that we have going vertically must be equals to M G finally we know that this component the horizontal component of this force must be equals to M V squared over R because that's the force needed for circular motion by the way this works for a car going around a banked track as well it's just that the force isn't up thrust it's just the reaction force from the track so what do we know this force to be well we know if we have this angle here then to find out what the resultant is we're not turning through the angles so we're going to use sign if you haven't seen my easy vectors trick video then have a look at that so we can say that this force is going to be equals to mg divided by because you know it's going to be bigger by sine-theta turn away from your sins and awaiting your sign so that's how we can find the resultant force from the weight we also know to the force can be calculated using the centripetal force as well it's going to be MV squared over R divided by cos theta because we're turning through the angle in this case if the force can be calculated using the weight and it can be calculated using the centripetal force then we can actually equate these two things together more often than not you'll just have to rearrange this to find then the radius of the planes circular path or the speed that is traveling at see if you can have a go at rearranging to find the speed pause the video if you want to go with that we know that the m's disappear there because we've got em on both sides what we can also do is take sine theta over to the other side here and we end up with G equals V squared over R times now we have sine theta divided by cos theta you might know from math that actually gives us tan theta finally if you want to get speed from this all we have to do is rearrange this and we end up with V squared over R equals G divided by tan theta finally taking the answer the other side and square rooting it we end up with the square root of GR over tan theta squeeze of the whole thing there let's go back to our loop the loop so here's the track coming in now let's have a think about what the support force is from the track at each point as the car is going round so we have it here here and here at the top not too concerned about this side because it's going to be exactly the same as this side now let's just have a thing about this bit here first of all whatever it is support for so I'm going to call it s of the track has to be we know the weight is pulling downwards so we don't really care about that because the support force is going towards the middle the support force is only needed to provide the centripetal force so we can say s equals MV squared over R at that point however what about here here we have a support force as well but the support force also have to hold the car up so more support is needed for the weight so in this case the support force is going to be MV squared over R but also there has to counteract the weight as well what about up here well this time weight is pulling down so it's almost like weight is actually contributing to the centripetal force so actually less support force is needed at the top because weight helps so that means that s in this case again is providing the force for circular motion so that MB squared over R but this time the weight is actually helping so we can take off mg so when it comes to any question like this with vertical circular motion and weight is involved just think is weight helping or is it hindering if it's hindering then the support force needs to be greater if weight is helping the centripetal force as it were and we can take it away from the support force so I hope you found this useful if you did leave a like leave a comment down below if you think I've missed anything or you have a question and I'll see you next time

Channel: Science Shorts

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Id: a2o2mzBvWbU

Length: 19min 0sec (1140 seconds)

Published: Mon Mar 06 2017