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### Course: Physics library>Unit 4

Lesson 1: Circular motion and centripetal acceleration

# Centripetal force and acceleration intuition

The direction of the force in cases of circular motion at constant speeds. Created by Sal Khan.

## Want to join the conversation?

• I'm still not able to digest the role of friction as a centripetal force in case of a car taking a turn. Doesn't it oppose the motion, rather than changing the direction? How does it actually function as a centripetal force? Looking forward to a helpful response.
• if a car in a racetrack is turning to the left(towards the center) its wheels will be turning to the right(away from the center)

https://qph.fs.quoracdn.net/main-qimg-cf054973c22da383a8d879e0bf11c3bb

the static friction allows the road to push back against the wheels of the car making it turn.
if there was no friction the car would slide straight or away from the center, to make it move in a circle friction must act inwards, so that's how it act as a centripetal force.
• is centripetal force a pseudo force?
• no not pseudo. Good question.

It is the name that we give to a force that causes an object to move in a circualr path. examples:

For the Earth around the Sun: Gravity IS the centripetal force
For a ball swinging around your head on string: Tension in the string IS the centripetal force.

Hope that clarifies
• what happens when you have uniform non zero acceleration
• I'm going to assume that you are questioning about Centripetal Force. The "Non zero" acceleration you are referring to is an acceleration that is either - acceleration or +acceleration but not 0 acceleration. If your meaning is - acceleration, the answer would be the car stays still since you cannot decelerate from initial velocity of 0 because the car is not applying force against gravity which is an conservative force and friction is an non-conservative force or if the car had some initial velocity, it would reduce its velocity to 0. If the car had some initial velocity and was decelerating, the centripetal force the tire supports would decrease and the centripetal acceleration would decrease since the car is slowing down. The centripetal force and acceleration changes since they only stay constant if the car's velocity was constant. Now, if you were referring to + acceleration, the friction of the tire would have to support more centripetal force and would increase since the velocity of the car is going faster. It would continue until the tire of the car cannot support enough force to turn it. The friction of the tire is given by the coefficient of kinetic friction times mass of the car times gravity or Greek letter mu (u with a line at the left)mg.

Hope this helped and your curiosity has been rewarded with a + 1 vote :)
• I have a doubt regarding the procedure used to find the direction of the ∆V vectors which is supposed to be in the direction of the centripetal force that is accelerating the body & changing it's direction at every instant. At s Sal copies & pastes 2 velocity vectors having the same magnitude but having different directions. Let us assume the second vector is after time interval Δt from the first vector. So during that time interval it experiences an acceleration due to the centripetal force and hence changes it's direction by an angle Δθ. So now we have a new vector with the same magnitude but at an angle Δθ w.r.t to the first vector. Now when we try to find the ∆V vector by joining the tip of these two vectors which are co-centric but have a certain angle between them, then geometrically it is not possible for the supposed ∆V vector to be at right angle to the initial velocity vector, or for that matter it can't be perpendicular to any of the two velocity vectors as is shown by translating the vectors at . And if it is not perpendicular it is no longer pointing to the center of the circe!! To make the ∆V vector perpendicular to the initial velocity vector, the second velocity vector has to be larger than the first one in magnitude as per the pythagoras theorem. Then it would no longer be a case of uniform acceleration. It would then be a variable acceleration and the magnitude of the second velocity would be larger. There could be some problem with the logic given in this video or may be I am confusing something. Would appreciate if you could clear my doubts on this matter...Thanks
• You are right. If you compared the first velocity vector with a different velocity vector other than the second one, you will find that the change in velocity is not perpendicular to the velocity vector, and therefore the acceleration won't be perpendicular. But you must keep in mind that that is the direction of the average acceleration! If you take into account two velocity vectors at a very small time interval "dt" and took the change in velocity(dv), you will be able to convince yourself that the direction of "instantaneous acceleration"(which is what we want) is towards the centre. Therefore a=dv/dt acts towards the centre. Note that the "d" in the dv and dt means a very small change.
(1 vote)
• So what IS the difference between centripetal force and centrifugal force?
If I'm understanding Sal's explanation correctly, centripetal force is a force that pulls object to the centre of the circle/gravity, then what is a centrifugal force?
• Centrifugal force is an apparent force that comes from looking at something from a rotating frame of reference. For example when you are on a spinning marry-go-round you feel like you are being pushed away from the center. This force you feel if you describe it from the viewpoint of the marry-go-round it is an outward force the centrifugal force.

If you look at this same marry-go-round from the viewpoint of the ground the force on the person is seen as a inward force making them travel in a circle instead of a strait line this is the centripetal force.
• Why is it that @ he draws the white arrow from the arrow head but in the circle he draws the white arrow from the bases of the coloured arrows?
• It does not really matter. Whether he draws it from the arrow head or the base, the laws of vector addition still make them both equivalent. The point is that all those change in velocity vectors point toward the center of the circle, making it a purely rotational motion. They would all point to the center whether or not the "change in velocity vector" (Delta V) is drawn from the base of the velocity vector or from the arrow on the velocity vector.

Also, the diagram to the right in the video begins to set you up for free body diagrams for objects rotating around a point, in which all forces will be drawn from the center of mass of the object.
• So, would a satellite be considered a perpetual motion machine?
• The satellite only revolves around the gravitational body if the gravitational body exists. That's not perpetual motion. However, if the gravitational body were removed and the satellite revolved around nothingness, it's perpetual motion.
• What happens when the velocity isn't constant?
• Then that is when tangential acceleration comes into play. We have the centripetal acceleration changing the direction of the velocity vector and when the tangential acceleration changing the magnitude of the velocity vector.
• Why are the change in velocity vectors placed perpendicular to the velocity vectors?