What is Circular Motion & Centripetal Acceleration in Physics? - [1-4-14] 

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Thank you for this video. The explanation on why the directions of acceleration and velocity can be different was very helpful.

Another fantastic emphasis on direction change in the velocity vector providing acceleration. They need to emphasise this in school.

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Near 18:00, to claim that when the radius r goes down, the acceleration goes up is INCORRECT. This is because linear velocity v is also a function of r. So, if the centripetal acceleration is written as r*omega^2 (instead of v^2/r), you find that the centripetal acceleration is actually proportional to r. Note that omega (the angular velocity) is independent of r.

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One equal angle between the two triangles. Angle between r1 r2 is theta where r1 =r2 = r is the same as angle between v1 & v2, where v1 = v2. One Side equal between the two triangles. v2-v1 is equal to r Two sides of one triangle are at 90 degree to the corresponding side of the other triangle.

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Excellent. You answered exactly the question I had in my mind: How can you have an acceleration if the velocity is the same Thanks a lot

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1) You were trying to demonstrate a body in UNIFORM circular motion which implies the magnitude of its velocity is CONSTANT but the direction is continually changing. Unfortunately, the circular motion you were demonstrating using an object tied to a string and whirled in a VERTICAL circular fashion had CHANGING magnitude and direction of velocity. The tangential velocity is greatest at the bottom, decreases as the object goes up along the circular path, least at the highest point and increases on its way down. Because the direction of velocity is always changing there arises a centripetal acceleration (a = v²/r) and a tangential acceleration (aₜ = ω² r) which is the result of a changing magnitude of tangential velocity. 2) It would really be much easier to explain the concepts of centripetal acceleration and centripetal force if Newton's Three Laws of Motion has been introduced to students much earlier on. For example, the formula for centripetal acceleration (F= mv²/r) is in fact derived from the formula Fₙₑₜ = ma (the 2nd law). Using the 2nd law, it is more meaningful to let students realize the net force causing the centripetal acceleration of a body in curvilinear motion.

The difference of the velocity delta V (= Vb-Va) will be pointing towards the center of the circle even if points A and B are not close by.

I just told u it's not going to be a perfect circle. Jason is so awesome.

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I have a very simple but question. Why doesnt the object collapse into the point. Since the centripetal force is an acceleration is increasing with time it should get to a point where its high enough to pull the object towards its centre. For example: The electron in an atom if not for its stationary state it should be pulled towards the nucleus since the proton and nucleus attract but what keeps it moving in a circular path is the fact that they have fixed energy called stationary States so they can't lose energy. But objects in the real world dont have fixed energy level so what keeps them in circular path? Another example is that if we change the mechanics occurring on the body interms of force, The centripetal force will be the F=m×a but converting the objects tangential velocity into force its F=0 since it has no acceleration.Resolving the 2 forces the object is supposed to move towards the center so why does it still move circular

Help me out here, please, but as you said at 12:40 "always pulling toward the center" can't possibly be true as that wouldn't create any force. What I believe you're actually doing is pulling PAST THE CENTER. If you truly watch what your hand is doing it's moving slightly outside and around the true center and leading the mass around an invisible or virtual cantilever depending on how large the motion of leading or pulling force's radius is, around that center, which oddly the orbit or pulling force is actually creating that center. A true center or singularity could never have a pulling force unless it had some mass or radius in order to wind and therefore apply tension to the tether. If you attempt to move anything by rotating a needle at the center of the tether, the mass at the end will not move because the lack of friction of the needle which is essentially tantamount to a true singularity and therefore cannot apply any force. There must be some radius which we would know as a hub, around the axis, in order to apply any force to the tether. Therefore, in order to apply force inward there must be a hub and you because there's a hub that force being applied is actually NOT toward the center but beyond the true center, OUTWARD, from the center and using the hub as a fulcrum. So, the leading angle of the power source, moving outward, depends on the rigidity of the tether which would determine the amount of allowable acceleration physically possible before the tether fails. As we all know, if you try to move something too quickly it just breaks. So, the idea of "always moving toward the center cannot be true." If it were true, you'd quickly find that true center and all force would stop. No, the more I think about this the more I think you're incorrect. Picture a mass on a rope, tethered by a pin - you apply force to the mass to create a velocity vector which will cause the mass to rotate around the center because of it's tether. The tether is truly pulling inward because of it's tensile strength but it's true center is not moving and has an essential singularity point, therefore no more force is or will be applied because there is no more "inward" physically, therefore to produce the force you're talking about here there must be force that is beyond the center and therefore OUTWARD of the center and leading the mass by ~181º or more depending on the rigidity of the tether. Wait, so if this is true, there can never be a true center. A true center would always result in a singularity and therefore no force. There must always be a hub in order to apply any velocity vector, and a hub means that the force is actually outward and beyond the center. Even if the tether is not physical it could never apply force from a true center and if it didn't have a true center then it must have a virtual hub or some sort of force by which leverage or force can be applied. Your planetary orbit model would suggest that at some point in time all planets will collide ... if gravity is pulling them toward the sun and there's nothing other than inertia preventing it, it will inevitable happen someday. When you talk about speed of rotation you're then assuming a constant by which you're judging two things, but what if that constant didn't exist? That constant of course is "time" but without that, literally everything is improvable and incorrect. All of this is judged against time and "time" is just a concept that we've given a value. Oh, I guess that works because all we're doing is attempting to explain something in a way that can't be disproven, so therefore assumed to correct but literally all of it is just made up stuff that we all agree to. Nothing is really real. There is only what we agree to be real. Ouch, my brain hurts. I'm sorry but when you run and turn it's not "pushing on the ground" that's moving you, it's friction. Without it, force is nearly impossible.

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I have a question and I am not sure how to explain it. I am looking for information on circular motion but I don't know the term used. Here goes. You have a pencil and draw an almost perfect circle. As the circle closes you keep the pencil drawing higher on the page then create another smaller circle above it, to the right and you continue doing this until you make a much larger circle. I don't know the term used for the mathematical symbol. It is also used in music as you go up a scale but then come back down a bit, then go back up the scale a little bit higher then come back down just a bit. and so one... until you end up at the top and reverse the process and slowly come back down the scale again to where you started... does this make sense to anyone? LOL Think of a moon circling a planet that circles the sun... that is the motion. But what is that called? There is a term for it? What is it? LOL

The more you learn, the more you realise that the more you really don't know. That is for sure with me. I know this is way ahead of me, but I still like seeing this kind of stuff. Watching this video made me wonder if earth's orbit speeds up as the orbit path narrows. Seems like it would.

Thanks a lot!

ur the best

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Them groundhogs are fast ;)

I did not understand how the both triangles are similar and pls explain the geometry behind it

Hi Jason,but you didn't explain how did you get v square ,,how did you get v square ? Please reply

Thanks. Chennai.

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Does the word Radial pointed inward have any relation to the word Radians used in Trigonometry ?

radius

a=v2/r

15x15

radius=diameter/2

a=225.0 m/s/22.5 m

diameter 45.0 m

a=(15.0m/s)2/r

a=(15.0 m/s)2/22.5 m

Nice 👍 Notifications are working again 👍

a=(15.0m/s)2/22.5m

a= 30.0 m/s/22.5m

45.0 m

scale

r=45.0m/2

a=10.0 m/s2

Why is it so that when you drive a car in circle your body want to move away from the center?

a=10.0m/s

225

Is this angular momentum?

r=22.5m

360 degrees

formula

accelerate

I'm still confused how it's really an acceleration, if it was really accelerating wouldn't the angular momentum constantly be going up(or down)? If you use some polar coordinate system, or combine the x and y coordinates in some way, that makes it obvious that the amount of force pulling to the center is constant, as well as the instantaneous velocity, you can obviously see nothing is increasing(decreasing) overall. It seems like you're just trading the change in direction in a circle for the change in position of something moving in a straight line. Does that mean that the definitions just lead to this misleading terminology?

m/s

H2'0 is water.

speed 15.0 m/s

asks acceleration dog rounds the turn

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some dog 45.0 m turn running speed 15.0m/s

diameter 45.0m