Centripetal acceleration
Centripetal Force and Acceleration Intuition The direction of the force in cases of circular motion at constant speeds
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- Let's say we observe some object--
- let's say for the sake of argument, it's happening in space
- It's traveling in a circular path with
- the magnitude of its velocity being constant
- Let me draw its velocity vector
- The length of this arrow is the magnitude of the velocity
- I want to be clear. In order for it to be traveling in the circular path
- the direction of its velocity needs to be changing
- So this time the velocity vector might look like that
- After a few seconds the velocity vector might look like this
- After another few seconds the velocity vector might look like this
- I'm just sampling. I actually could've sampled after a less time and it would be right over there
- but I am just sampling sometimes as it travels around the circle
- After a few more seconds the velocity vector might look something like that
- I want to think about what needs to happen
- what kind of force would have to act
- in particular the direction of the force would have to act on this object
- in order for the velocity vector to change like that?
- This remind ourselves if there was no force acting on this body
- this comes straight from Newton's 1st Law of motion
- then the velocity would not change
- neither the magnitude nor the direction of the velocity will change
- If there were no force acting on the subject
- it would just continue going on in the direction it was going
- it wouldn't curve; it wouldn't turn; the direction of its velocity wasn't changing
- Let's think about what the direction of that force would have to be
- and to do that, I'm gonna copy and paste these velocity vectors and keep
- track of what the direction of the change in velocity has to be
- Copy and paste that
- So that is our first velocity vector
- Copy all of these. This is our second one right over here
- Copy and paste it
- I'm just looking at it from the object's point of view
- how does the velocity vector change from each of these points in time to the next?
- Let me get all of these in there
- This green one
- That. Copy and paste it
- That. I could keep going, keep drawing velocity vectors around the circle
- but let me do this orange one right over here
- Copy and paste
- So between this magenta time and this purple time
- what was the change in velocity?
- Well, we could look at that purely from these vectors right here
- The change in velocity between those two times was that right over there
- That is our change in velocity
- So I take this vector and say in what direction was the velocity changing
- when this vector was going on this part of the arc
- It's roughly--if I just translate that vector right over here
- it's roughly going in that direction
- So that is the direction of our change in velocity
- This triangle is delta; delta is for change
- Now think about the next time period
- between this blue or purple period and this green period
- Our change in velocity would look like that
- So while it's traveling along this part of the arc
- roughly it's the change in velocity if we draw the vector starting at the object
- It would look something like this
- I'm just translating this vector right over here
- I'll do it one more time
- From this green point in time to this orange point in time
- and obviously we're just sampling points continuously moving
- and the change in velocity actually continues changing
- but hopefully you're going to see the pattern here
- So between those two points in time, this is our change in velocity
- And let me translate that vector right over there
- It would look something like that
- change in velocity
- So what do you see, if I were to keep drawing more of these change in velocity vectors
- you would see at this point, the change in velocity would have to be going
- generally in that direction
- At this point, the change in velocity would have to be going generally in that direction
- So what do you see? What's the pattern for any point along this circular curve?
- Well, the change in velocity
- first of all, is perpendicular to the direction of the velocity itself
- And we haven't proved it, but it at least looks like it
- Looks like this is perpendicular
- And even more interesting, it looks like it's seeking the center
- The change in velocity is constantly going in the direction of the center of our circle
- And we know from Newton's first law
- that if--the magnitude could stay the same but the
- velocity change in any way, either the magnitude or the direction or both
- there must be a net force acting on the object
- And the net force is acting in the direction of the acceleration
- which is causing the change in velocity
- So the force must be acting in the same direction as this change in velocity
- So in order make this object go in this circular
- there must be some force kind of pulling the object towards the center
- and a force that is perpendicular to its directional motion
- And this force is called the centripetal force
- Centripetal
- Not to be confused with centrifugal force, very different
- Centripetal force, centri- you might recognize as center
- and then -petal is seeking the center. It is center seeking
- So this centripetal force, something is pulling on this object towards the center that
- causes it to go into this circular motion
- Inward pulling causes inward acceleration
- So that's centripetal force
- causing centripetal acceleration
- which causes the object to go towards the center
- The whole point why I did this is that at least it wasn't intuitive to me
- that if you have this object going in a circle
- that the change in velocity, the acceleration, the force acting on this object
- would actually have to be towards the center
- The whole reason why I drew these vectors
- and then translate them over here and drew these change in velocity vectors
- is to show you that the change in velocity is actually towards the center of this circle
- Now with that out of the way, you might say, well, where is this happening in in everyday life
- or in reality in some way it perform
- And the most typical example of this and this is something that I think most of us have done
- when we were kid if you had a yoyo
- My best attempt to draw a yoyo
- If you have a yoyo and if you whip it around on a string
- you know that the yoyo goes in a circle
- Even though its speed might be constant, or the magnitude of its velocity might be constant
- we know that the direction of its velocity is constantly changing
- It's going in a circle and what's causing it to go in a circle is your hand right over here
- pulling on this string and providing tension into the string
- So there's a force, the centripetal force in this yoyo example is the tension in the string
- that's constantly pulling on the yoyo towards the center
- and that's why that yoyo goes in a circle
- Another example that you are probably somewhat familiar with or at least have heard about
- is if you have something in orbit around the planet
- So let's say this is Earth right here
- and you have some type of a satellite that is in orbit around Earth
- That satellite has some velocity at any given moment in time
- What's keeping it from not flying out into space and keeping it going in a circle
- is the force of gravity
- So in the example of a satellite or anything in the orbit
- even the moon in orbit around the Earth
- the thing that's keeping an orbit as opposed to flying out into space
- is a centripetal force of Earth's gravity
- Now another example, this is probably the most everyday example because we do it all the time
- If you imagine a car traveling around the racetrack
- Let's draw a racetrack. If I have a racetrack
- Before I tell you the answer, I'll have you think about it
- It's circular. Let's view the racetrack from above
- If I have a car on a racetrack. I want you to pause it before I tell it to you
- because I think it's an interesting thing think about
- It seems like a very obvious thing that's happening
- We've all experienced; we've all taken turns in cars
- So we're looking at the top of a car. Tires
- When you see a car going at a constant speed
- so on the speedometer, it might say, 60 mph, 40 mph, whatever the constant speed
- but it's traveling in a circle
- so what is keeping--what is the centripetal force in that example?
- There's no obvious string being pulled on the car towards the center
- There is no some magical gravity pulling it towards the center of the circle
- There's obviously gravity pulling you down towards the ground
- but nothing pulling it to the side like this
- So what's causing this car to go in the circle as opposed to going straight?
- And I encourage you to pause it right now before I tell you the answer
- Assuming you now unpaused it and I will now tell you the answer
- The thing that's keeping it going in the circle is actually the force of friction
- It's actually the force between the resist movement to the side between the tires and the road
- And a good example of that is if you would remove the friction
- if you would make the car driving on oil or on ice
- or if you would shave the treads of the tire or something
- then the car would not be able to do this
- So it's actually the force of friction in this example
- I encourage you to think about that
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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