this video is for those of you who are studying for a tests on uniform circular motion so what I'm going to do in this video is I'm going to give you a quick review of the formulas that you need to know for this chapter so uniform circular motion so we're dealing with objects that are moving in a circle now key word uniform these are objects that are moving at constant speed so let's say if the the object is going in the counterclockwise Direction the velocity Vector is going to be Upward at this point and it's going to be an acceleration vector known as centripetal acceleration that always points towards the center of the circle so when the object is here the velocity Vector will be directed West but the centripetal acceleration will always always be directed towards the center of the circle now the cental acceleration it's equal to the square of the Velocity ID by the radius of the circle so as you double the velocity 2^2 is 4 the centripetal acceleration increases by a factor of four now keep them keep this in mind the object is moving in a circle at constant speed but because it's changing direction the velocity changes and whenever the velocity changes there going to be an acceleration because acceleration is the change in velocity divided by the change in time remember velocity is speed with Direction the magnitude of velocity is constant for uniform circular motion but the direction changes and so because the direction is changing the velocity is changing which means that there is an acceleration so anytime you have any object that moves in a circle you're always going to have some kind of centripetal acceleration now according to Newton's SEC according to Newton's Second Law the net force acting on an object is equal to the mass times the acceleration so anytime you have an object moving in a circle there's going to be something called a centripetal force and it's equal to the mass times the centripetal acceleration so replace an AC with v ^2 R we get the formula for the cental force which is m v^2 / R so make sure you add these two formulas to your list and you could also put this one as well okay let's just redraw this picture real quick now going back to this equation let's talk about how we can calculate the velocity for an object moving in uniform circular motion now we know that velocity is displacement over time and the distance that the object travels in a circle is going to be the circumference of that Circle and the circumference is 2 pi * the radius the time it takes for the object to make one complete revolution around a circle that is known as the period which is capital T both lowercase T and capital T they're measured in units of time like seconds minutes or hours the frequency is 1 over the period now if we were to take this equation and plug it in for V we will get that the centripetal acceleration is 4 pi^ 2 * r/ T ^2 so that's how you can calculate you could use this formula to calculate the centri acceleration if you know the radius of the circle and the period of the object in circular motion if you know the period you can also calculate the velocity using this formula now the period is equal to the time divided by the number of Cycles so for instance let's say if it takes 30 seconds for this object to make five Revolution the period would be 30 seconds divid those five Cycles so that's 6 seconds per cycle so the period will be 6 seconds the frequency is the reciprocal of that it's the number of Cycles divided by the time the frequency is measured in hertz or one / seconds now sometimes you may need to calculate the tension of an object that's moving in circular motion so let's say you have a ball with negligible mass and it's attached to a rope and it's moving in a circle and we want to calculate the tension force at these different points let's say at Point a b c and d at points A and C the tension force is approximately equal to MV ^2 R in those cases the centripetal force is provided by the tension force in a rope now at Point D at the bottom of the vertical Circle the tension force is going to be the sum of the centripetal force and the weight Force because not only does the Rope have to support the weight of the object at Point D but it also needs to apply a centripetal object to turn it from point B to point C now at point B the tension force is going to be the weakest and it's going to be the difference between mv^2 / r the centripetal force and the weight Force so make sure you understand this at Point D the tension force is at a maximum at point B the tension force is at a minimum now let's say if you have a similar situation but instead of the ball moving in a vertical Circle let's say if it's moving in a horizontal Circle if it's moving fast the tension force is going to be approximately equal to the centripetal force but let's say if it's not moving very fast such that it's not very horizontal there's an angle to it so let's say we have this situation but it's sort of moving in a horizontal Circle so this is going to going to be the tension force it's going to be an X component which is usually going to be significantly larger than the Y component and we have an angle here in this case the tension force in a rope is going to be the Square t of tx^ 2 + T y^2 now notice that TX is horizontal and it points towards the center of the circle so TX provides the centripetal force which is MV ^2 r if it if this object is moving fast enough this angle is going to be close to zero and T is going to be approximately equal to TX which is the cental force that's why I have this approximate symbol but if it's not moving fast enough and you could see a significant angle then you need to calculate T this way now Ty supports the weight of the object so Ty Y is going to equal mg and tangent Theta is going to equal the ratio of Ty y over TX so using these formulas you can calculate the tension in the Rope now for those of you who want to see how to use these formulas with example problems feel free to check out the links in the description section below I'm going to be posting some other videos on this chapter where you can practice practice using these equations so you know what to do on an actual exam now there's other formulas but there's one more formula I want to give you and this has to do with let's say if you have an object that is moving on a hill and let's say in a valley at the bottom of the valley let's say it moves with speed V and we want to calculate the normal force exerted by the ground on the object and also when it's at the top of the hill so at the bottom of the hill the normal force is going to be the sum of the centripetal force plus the weight Force so keep in mind this object it's turning and anytime it changes Direction like that there's a centripetal force that is directed towards the center of the circle because there's a centripetal acceleration that points towards the center of the circle in this case the center of the circle is over here so this will be like the radius of this circle and here is the cental force pointing towards the center of the circle so at the bottom of the hill or at the Val the normal force is going to be at a maximum because it has to support the weight force and it has to provide the centripetal force to cause the object to turn at the top the normal force is going to be the difference between the weight force and the centripetal force if the object is moving too fast such that this quantity is greater than this quantity where you get a negative result what that means is that the object loses contact with the ground and it's basically flying off if you get a positive result for the normal force that means the object remains in contact with the ground but if as V increases if it gets too high the normal force that you'll get will be negative which means that there is no normal force the object is off the ground at that point so at the top the normal force will be at a minimum for this kind of problem so I'm going to stop the video here and if you want to see an example problem on this particular situation feel free to check out the links in the description section below I have a video that's entitled normal force on a hill um you can look it up on YouTube but you'll also find it in the description section so feel free to take a look at that and thanks for watching