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centripetal force and centrifugal force easy concepts
Today is most important topic Centripetal force and centrifugal force so far in circular motion previous post we have studies only about kinematics part which deals with angular displacement,angular velocity,angular acceleration,centripetal acceleration,tangential acceleration you can refer previous post centripetal and tangential acceleration but in this topic dynamics of circular motion which deals with centripetal force and centrifugal force means we will find out the cause of circular motion and we know from Newton’s laws cause of motion is force so here in circular motion centripetal force and centrifugal force we will study very interesting and easy concepts.
any particle of the world do circular motion its velocity changes every time due to change in direction whether its speed is constant or speed may change but condition for circular motion its velocity direction always be change its magnitude may change or may not change but direction always be change and we know that due to change in velocity acceleration is created hence it is clear that if body is doing circular motion then acceleration is there and we know that due to change in velocity direction acceleration is created and this is called centripetal acceleration and its direction is always towards the center of the circle along the radius it is denoted as a𝒸 in previous post we have already studies formula for a𝒸 = v²/r = r𝛚² where v is tangential velocity r is radius and 𝛚 is angular velocity now important point can you tell me which quantity create acceleration answer is force create acceleration or acceleration create force this is just like question which one first came on the Earth hen or egg hence the correct answer is force create acceleration because when we apply force then body start accelerate and due to acceleration velocity change hence in circular motion if centripetal acceleration is there so it is clear that centripetal force created centripetal acceleration i hope that you should not have any doubt about centripetal force concept now and this is vector quantity hence it has direction so from Newton’s second law we can write
F = ma hence direction of force will be same as direction of acceleration so centripetal force direction is always towards the center of the circle along the radius as shown in above figure and its direction always changes and always towards the center of the circle hence this is power of dynamics which tell us the cause of centripetal acceleration created due to centripetal force now what will be formula of centripetal force hence from above formula F = ma put here a = a𝒸 = v²/r = r𝛚² so F𝒸 = mv²/r or F𝒸 = mr𝛚² so whenever there is circular motion anywhere in the world there may be a centripetal force but wait and wait there is no any centripetal force existence in the world this is truth you can refer my previous post for different forces in the world you will get here all force in the world no any force name centripetal force then you will think what is this and which is centripetal force ? then answer is actually some other force made centripetal force or some other force which behaves as centripetal force for example a bob is tied in a string and rotate the bob with hand the bob will rotate in a circular path a tension will develop in the string towards the center this tension is called centripetal force hence its actual definition is “the net force towards the center is called centripetal force” very important point note is the resultant force towards the center is given the name centripetal force take other example Earth and Moon we know that Moon rotate around Earth means Earth attract Moon with gravitational force this gravitation force towards the earth will become centripetal force you can’t apply a new force name as centripetal force the net resultant any force towards the center will be given name as centripetal force now question arises is this force is imaginary or real correct answer is this is real force if it will be imaginary then no any body or particle can do circular motion actually we have made the concept that the net force acting towards the center given name as centripetal force i hope now your concept is clear for this force see below some question.
As from the above arrangement we have to find tension in all string T, T1, T2 hence lets start from 3kg block see FBD T2 tension in string acting towards center hence it will be equal to centripetal force in radius of 3m important point angular velocity for all three masses will be same and is 2 rad/s because all three are moving same angle in same time but remember linear velocity for all three masses will be different because v =r𝛚 here radius for all three block is different so F𝒸 = T2 = mr𝛚² = 3*3*2² = 36N
now for 2kg block see the FBD here net force towards the center will be centripetal force F𝒸 = T1 – T2 and it is moving in 2m radius so F𝒸 = mr𝛚² = T1 – T2
2*2*2² = T1 – 36
16 = T1 – 36 or T1 = 16+36 = 52N T1 = 52N
now for 1kg mass similarly we can use equation from FBD
F𝒸 = T-T1
mr𝛚² = T – 52
1*1*2² = T -52
4 = T-52 or T = 4+52 = 56N hence T = 56N
hence we can calculate applying concept of centripetal force net force towards center.
Centrifugal force : it is a pseudo force we know that pseudo force acts in non inertial frame of reference now non inertial frame of reference is that frame of reference where observer is observing from an accelerated frame of reference means acceleration of frame of reference is not zero where Newton’s second law of motion F = ma is not valid because this law and formula is only valid for inertial frame of reference means non accelerated frame of reference acceleration is zero this frame of reference is called inertial frame of reference in non inertial frame of reference pseudo force always acts opposite to original acceleration direction you can see the first figure where observer is sitting inside car
on circular motion will feel a centrifugal force opposite to center of the circle and its value will be same ma where m is mass of the observer and a is acceleration of rotating frame of reference and centrifugal force direction will be opposite to original direction of acceleration hence formula for centrifugal force = ma = mv²/r = mr𝛚² and direction is away from the center and observer is sitting on rotating frame of reference this is all about the centrifugal force its value is same as centripetal force only frame of reference is changed in centrifugal force now we will continue in next post i hope you have enjoyed learning centripetal force and centrifugal force easy concepts thanks for reading and sharing.
date 27th Sep 2018