in this video I'll talk about car on a banked road so you can see here a car there are many cars and speaking one card here this cars are moving on a bank road or on a kata road and assuming there is no frictional force and in order to negotiate the banking or the tilting what should be the of the maximum speed of the car we need to find out the banking angle at which the car can move with the maximum speed and let me tell you if the car is at all that speed then the car will skid away so there is the maximum limit of the speed and we need to find out that maximum speed limit so here is the problem a car it's going around a bank curve and the radius of the the curve or the circular path is 150 meter and and the car should move at 75 kilometers per hour then now if you are an engineer or a future engineer what is what should be the angle of banking and then and here of course we assume there is no frictional force and we need to calculate this one before jumping into the answer I would like to give you a little little bit mathematical background with this one so let's say this is a car here and the car is moving on a tilted roller or the bank to roll so let's say the angle of banking is Theta and in order to derive the relationship between the velocity and the banking angle we need to understand the free body diagram so the weight of the car is all of its downward which is the mg and the normal force is n which is perpendicular to D the the ramp so this is the normal force in order for the car to move into a circular track or a circular path there must be some sort of force to provide the necessary centripetal force so what going to do we're going to resolve this normal force into two components two rectangular components the one is n sine theta and the other is n cosine theta and here as I mentioned this is the banking angle theta this angle also stood with a banking angle how come so how do we know that this angle is Theta not this angle so the angle if the and this theta is the angle between this plane this plane and this plane so if I draw a perp so the angle between the perpendicular between these two lines will also be theta so this green line is perpendicular to this line and this purple one is a perpendicular to this slope so the angle between them has to be theta so now as this angle is Theta this should be the cosine component and cosine theta and this one should be n sine theta so these two have a different purpose now so the norm mg has to be equal to ten cosine theta or the normal force onto the car is balanced by the weight and there is no movement in the vertical direction because the N cosine theta is exactly balanced by the weight of the car and the purpose the N sine theta provides the necessary centripetal force okay this purpose the necessary centimeter without this force the car would not be a to move in on a banked road and here is the equation and a cosine theta as I mentioned is mg + n sine theta is the centripetal force the centripetal force is MV squared over R so this is the centripetal force now if I divide this equation by this equation and an N will cancel and sine theta over cosine theta will be tangent theta and we have to divide this side as well and the mass and mass will cancel and we will left with V squared over R Z so this is the relationship between the velocity and the the banking angle so we have now that tangent theta is equal to V squared over R G and we are we need to find out the theta at which the car can move with a maximum speed of V so theta will be tangent inverse ax squared over V squared over R T the velocity or the speed or say is 75 kilometers per hour and I'm changing 75 kilometers per hour to meter per second and this comes out to be 28 20 point 8 meter per second so when you just plug in all the information twenty-eight point twenty point eight and the radius is hundred fifty the gravitational value is nine point eight the angle will get is sixteen point four degree this is the angle at which the car can safely negotiate the or the car can safely move on the circular path at this speed so this is it from today's this lecture again if you have any questions write down your question in the comment section below and do not forget to Like share and subscribe the channel thank you very much