Principle of physics used in the lift of skateboard What is the principle of physics used in this popular stunt?
Initially, I thought aerodynamics due to an increase in the angle of attack, but its magnitude is not sufficient to balance the whole body and skateboard. Please, can anyone help me to get about it?

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*Animation:

 A: Let us first examine all possible mechanisms for forces that have an upward component.

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*Lever mechanism

*Flex in the tail

*Reaction of the wheel

*Front foot drag

Out of all these obviously the lever mechanism causes the most upthrust. This is backed up by the fact that this portion of the ollie makes the largest displacement.
Flex of the tail (mainly the J-shaped ones) could cause a reasonable  upthrust. But it isn’t a necessity. Same with the reaction of the wheel.
Now coming to the front foot drag. Due to the board being diagonal for the portion of the front foot drag, any lift provided will be diagonal. This means that the board must have gain a forward momentum as well. Since in the gif presented by OP there isn’t significant forward momentum, we can say that the lift provided by the foot dragging is negligible.
However the foot drag is essential for the ollie. Just not for the upthrust. To keep the board from over shooting it’s backwards rotation, there has to be a mechanism to keep it in check. Moreover without the front foot drag, there would only be one point of contact between the boarder and the board which makes the system highly unstable.
Here’s video evidence thanks to Eric Duminil’s comment under this answer that shows that the front foot drag isn’t essential for upthrust.

A: The skateboard is able to lift off the ground because of the momentum imparted to it by the skateboarder pushing down on the kicktail. The skateboard acts as a lever around the rear wheels, so when the kicktail is pushed down, the center of mass of the skateboard rises up. If you do this fast enough, the skateboard's center of mass gets enough upward momentum to lift the entire skateboard off the ground.
To set up a similar experiment, lay a ruler or pencil so it hangs over the edge of a table a small amount, hit down on the free end, and watch it fly up into the air. You may notice that the object not only flies up but also across the room toward the end you hit. The impulse imparts both vertical and horizontal momentum, which you can see in the first part of the skateboard clip as the center of the board moves both upward and backward.
The skateboarder then uses their front foot to stop this horizontal/rotational motion of the board and keep it under their feet, which is possible because the skateboarder has much more mass/inertia than the board. Because the skateboarder is tens of times as massive as the board, they are easily able to manipulate its momentum with their body, while changing their own momentum relatively little (if you look closely, you can see that both the skateboard and skateboarder do, in fact, land slightly behind the point of liftoff). If they just stomped on the kicktail without doing anything else, the board would arc upwards and backward, flipping end over end through the air.
There is nothing related to aerodynamics at play here, this trick could be performed exactly the same way in a vacuum.
EDIT: There seem to be some other factors at play that I've missed here. In particular, the front foot can add some lift to the board as it slides forward to the nose. As the board leaves the ground and rotates up into the front foot, it produces a normal force, which allows the front foot to impart a frictional force parallel to the surface of the board. This won't get the board off the ground in the first place (since friction is always parallel to the board), but once the board is oriented somewhat upright, the board can be pulled further upward by the front foot. Thanks to @Todd Wilcox for pointing this out.
A: Others here have given great answers about the physics behind this, but I would like to describe the actual approach of this skateboard stunt known as an Ollie. I'm a skateboarder myself and I regularly use this maneuver to jump onto and over various obstacles including curbs, boxes, and metal rails. Think of the skateboard as a simple seesaw in a way. Weight on one end tilts it down, and weight added to the other end levels it out, although the actual process is a little more complicated and takes thousands of attempts to master.
An Ollie starts with the rider jumping up and pushing the tail downwards in a snapping motion with the back foot. This causes the skateboard to pop up to an extent and start to stand up on it's tail. The actual "lift" of the skateboard is mainly generated by the front foot dragging across the top of it to pull it upwards with the body. Once the front foot hits the nose of the board, the foot is moved forward to level the board out in the air. Doing so allows the board to stay as close to the feet as possible to maintain full control over the stunt throughout the entire process. A lot of beginners will forget to move the front foot up/forward which leads to the board briefly rising up on the tail and then falling back down without leaving the ground.
Notice the position and angle of the front foot before the jump is initiated. The further back the front foot is, the more the board will raise up with the jump as this allows the board to stand up more ("increase in the angle of attack") before being pulled upwards with the front foot. Having the foot slightly angled makes it easier to keep the outside of the foot in contact with the board as the foot is moved upwards and forward.
A: Updated Answer based on comments by @ToddWilcox that actually know more than me about this.
The answer by @NuclearWang is correct, but I wanted to illustrate the process a bit. At least the initial part that sets things up for the stunt.

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*Stage I

At this stage, the foot pushes downwards, but the reaction from the ground is greater because the center of mass (yellow dot) must move upwards, due to the kinematics of where the pivot is. For the whole time before the riders foot touches the ground, the center of mass of the board is accelerating upwards (acquiring vertical momentum)


*Stage II

This is the part I missed originally. The back foot causes rotation which is resisted by the front foot, while the foot is sliding upwards causing the sliding friction to add to the lift on the skateboard. This is important as kinematically the rotation of Stage-I can only lift the center of mass so much, and then it stops. To accelerate upwards more, a lift force is needed.


*Stage III

Once enough vertical velocity (yellow arrow) is accumulated by the center of mass and the end of the board strikes the ground, this reaction causes the wheel to lift off. At this point, if the board was allowed to continue to rotate it would pivot about its end launching itself between the rider's legs (not pleasant). At this point the rider's other foot stops the rotation with a slight nudge, leaving only the vertical motion allowing for the board to lift off completely.


*Stage-IV
From this point on the rider has to actively maintain the orientation of the board as it comes down so that it lands in a way where they can continue riding on it. Overall this stunt involves a carefully practiced choreograph of pushes and pulls on each leg to make the board leap into the air.
A: It's not so hard to understand what causes the upward jump (of course you have to jump in the right way to provide a torque on the board; that's something that one learns instinctively in time). But why does the board stays all the way close to the boy's feet?
As you can see in the clip, by pushing with his right (left in the clip) against the back of the skateboard, which causes the board to rotate. With his left foot, he stops the rotation and the reaction of the board is to stop rotating (it has to conserve it's kinetic energy though, so the rotational kinetic energy is converted into kinetic energy of a linear moving object, which can clearly be seen in the clip; the motion of the board starts with rotating and ends up moving linearly, staying parallel to the surface) thereby being able to stay close to his feet. The right (left in the clip) side of the board after the reaction, moves upwards after the guy has stopped it with his left foot.
A: The critical element is a conversion from angular to linear notion via an impulse created by pinning first the back wheel then the back tip then releasing back tip. I think @nuclearwang answer is very close but not clear enough.
Look carefully at the video and notice that until the back tip of the board touches the ground, the board is purely rotating around the back wheel. There is no horizontal movement of the back wheel before the back tip hits the ground, the wheel stays in place (although a small amount of horizontal motion would be fine - it would just take away from the attainable height).
So the answers that show an arrow up for center of mass, before back tip hits ground, are wrong. The center of mass is moving in an arc around the back wheel.
Then the back tip hits the ground. Let's call this time Tc. This event is critical, as the ground cannot move, so when it hits the ground it has to stop; all momentum, which is purely angular before Tc, is transferred to the back wheel, as a force normal to the surface. This basically converts some angular momentum to linear.
[[Image here to be added later - the app gives error when I try to upload it]]
But not all of it. Basically from Tc onwards, the skateboard would lift and rotate if you did nothing else to it. This includes removing the force you were applying at the back.
Then by applying the right amount of force at the front the board after the back wheel has left the ground, the angular rotation can be decelerated to 0.
What takes a lot of time to learn is coordinating the removal of force at the back so the back can lift off the ground, with application of force at the front sufficiently soon after the lift off, in the right amount to decelerate rotation.
Interestingly, having that little kink near the end of the board means you can get higher angular momentum at time Tc. Indeed it takes less time for straight tail to hit ground, than a tail with an upwards kink, hence more time to apply force at the tail hence greater velocity reached at time Tc. This velocity goes to 0 at Tc, thus the greater this velocity the greater the counter impulse force that will be applied at the back wheel at Tc.
I don't have my computer here but I'll see if I can sketch something to illustrate these.
A: In the video/gif provided, you can plainly see that the board does not actually start to move up into the air until the foot starts dragging.
I puzzled over this for a long time until I watched my son try to learn to ollie and watched instructional videos with him. The physicsy answers here are unfortunate attempts at overthinking.
I worked with my son for a long time on this by watching him very closely and making videos. Getting his board into the air relied entirely on the foot slide.
So, @Max Green's answer is actually correct.
I challenge anyone who disagrees to try to perform an ollie with a teflon deck and teflon shoes. You can't.
What I love about this question is that physicists always try to talk about N3 and the board popping up due to a reaction force. Meanwhile, skilled boarders talk about what they are ACTUALLY doing, which is using friction to slide the board into the air.
And this is amazing because, during the very slow-mo videos they use to support their theory, at the very moment they are discussing how the board pops into the air, they completely miss the boarder's foot sliding up the board imparting upwards momentum through the friction interaction.
Physics:

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*Great video about the intermediate axis theorem, but watch the dude's foot when launching the board. https://www.youtube.com/watch?v=yFRPhi0jhGc

*https://www.youtube.com/watch?v=zAsdpRHdpDM

*https://www.youtube.com/watch?v=sfbiO9dAGBQ
Boarder:

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*https://www.youtube.com/watch?v=vLrsMflKaDw

*https://www.youtube.com/watch?v=XLVraCnI5Kc

*https://www.youtube.com/watch?v=jDZhiMMxlgM
Aaaaaaaaand: Physics of a skateboard ollie
A: I have an answer totally different than all the others. Odds might be low that it is right but I want to throw it into the ring.. I came up with this answer after watching many of the videos in the various answers and comments but will refer only to the video in the question.
disclaimer: I can't do an ollie. I tried years ago but could never nail it, so take what I say with a grain of salt. Some of my comments will be peppered by what I personally found difficult about the trick when I was trying to learn it.
Question: If I drop or throw something on the hard ground why does it bounce back up?
Answer: Assume the ground is a rigid body and doesn't move. If I drop something on the ground that means it initially has kinetic energy. Let's assume there aren't appreciable friction losses (so that the thing I am dropping isn't squishy, imagine dropping something like a bouncy rubber ball or steel ball as opposed to a blob of pudding). Well, after the ball hits the ground it could just stop instantaneously. But this would violate conservation of energy. Where does the energy go? The answer is that the ball (bouncy ball or steel ball) compresses slightly and the kinetic energy (which came from gravitational energy) is converted into compression energy. The ball then decompresses accelerating upwards, regaining kinetic, and then eventually gravitational potential energy.
How do I think an ollie works? In short, the skater uses their front foot to thrust their body upwards while almost simultaneously using their back foot to "throw" the board at the ground. If the timing and forces are all right the skater continues upwards and the board hits and bounces (or pops) off the ground following the rider into the air.
In more detail, follow along with video in question:

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*Rider is standing on skate board. front foot a little forward of the center of the board. Rear foot behind the back axle.

*Rider compresses legs and then jumps (converting elastic to kinetic energy of their own body). In particular, the skater's body is able to get air due to the jumping because of their front foot which is between the two axles. The front foot is like doing a one legged jump off of regular ground.

*The rider is also applying a downward force with the back foot. In addition to given the rider upward thrust this foot also serves to put a downward force on the back of the board creating a lever motion about the back wheels. In particular, if the riders front foot is starting to leave the board and the back foot is still applying a force this imbalanced force will cause the board to lever upwards.

*back of the board is now moving rapidly towards the ground and the skaters front foot is moving upwards because of the jump. The rider must now STOP applying a downward force with their back foot. In the video it looks like this is accomplished by ensuring their back hip is so high in the air (due to the jumping with their front foot) that their back leg is fully extended and unable to apply downward forces before the moment the back of the board hits the ground. With the rider no longer applying downward forces the back of the board is free to hit the ground with high speed causing flexion of the back of the board** (note the cantilevered bend on the front and back of the board, I suspect in addition to grip this gives the board some springyness that helps it "pop") to convert kinetic into elastic energy. The board then bounces or pops off of the ground, following the rider into the air.

I think at this point the main steps to get the board off the ground are described. In fact, the question only asks about the physics to lift the skateboard. I don't think anyone is confused about how the skater manipulates the board in the air by applying forces with their feet.
So how does the board come off the ground? The skater imparts kinetic energy to the board and then when the board hits the ground that kinetic energy is converted into spring energy which is converted back into kinetic energy and then finally gravitational energy as the board rises up. The trick seems to be* making sure the skaters feet are moving upwards already by the time the board is ready to bounce up into the air.
Regarding the toe drag: Some of the authors in this post make compelling arguments for the toe drag, but alas, after looking at many of the videos I have to say that I'm not convinced it is the main mechanism for getting the board off the ground. Rather, I think the toe drag is probably a very useful technique for skaters to 1) effectively manipulate and control the position and alignment of the board while the skater and the board are airborne and 2)  perhaps it helps get the timing right for the jump and release of downward force with back foot. That said, it is certainly plausible that the toe drag does apply some upward fore on the board and helps keep the rider's feet registered with the board throughout the air to microcorrect for differences in jump speed of the rider and board. I just don't think the toe drag could provide enough force to get the board that high in the air given how small the friction force must be and how heavy the board is.
*At least this is the part that sort of gave me trouble when I was trying to do an ollie in the past.
**See 1:26 in the skateology video, it looks like there is also some spring energy which is loaded into the trucks that provides some pop at the moment the board pops off the ground.
