Absolutely, that is what you should expect to happen. And it does The final solution is a little more involved than just being uniform rotation around the vertical axis. Keep in mind, however, that the top is now rotating around two different axes. Let's see how this happens. This is true for all but the most oddly shaped tops.
Convince yourself that this is the case. In circuits more current flows through paths with lower resistance. Likewise in mechanics more energy is transferred to the component with lesser inertia. Now, conservation of angular momentum requires that there be a torque corresponding to this increase.
The effect of this induced torque is to cause the falling top to start swinging back upwards. In this way, instead of a spiral, the tip of the top traces out something like a cycloid as it precesses around the central axis. I would not have known of this rather elaborate dynamics if not for one of Feynman's lecture volumes Part I, I think where this question is considered in great detail!
The above write-up is a little on the hand-wavy side and there probably are errors in my reasoning.
For the full kahuna look up the Feynman lectures! When it is spinning its angular momentum is quite high. By conservation of angular momentum the spinning top is then more stable against small torques like the action of gravity on the top. You can find a detailed discussion on this page of Hyperphysics. All the explanations given involve conservation of angular momentum, which is perfectly correct, but I feel that people with no thorough background in physics and mathematics will be left unsatisfied with this.
Is there a way to explain conservation of angular momentum in terms which would be understandable to the layman? It's a pedagogical problem I have given a lot of thought and I have yet to find a satisfactory answer. Surely, you need to start from something, some basic axiom that the person will be willing to accept at face value.
I thought about using either the law of action and reaction or conservation of momentum. I think these are relatively easy to describe "pictorially". But going from these to angular momentum using a vector product, is a mathematical procedure I'm not sure I can explain to someone who doesn't know anything about math.
So, this should be circumvented in some way by a nice visual example again to make things clearer and I haven't found not. The point is that conservation principles are not generally intuitive. For example, why should energy be conserved? One must have a grip of the dynamics involved in order to understand them. Anyway, the precession of the spinning top doesn't have to do with the conservation why angular momentum.
It has to do with the strange nature of torque and its interaction with angular momentum. When a force acts on a spinning top, it excerpts a torque perpendicular to the plane defined by the axis of the top and the direction of gravity, which is spinning vertical plane. That direction is horizontal.
On the other hand, the torque is the rate of change of angular momentum. That means that the direction of the torque is the direction towards which the vector of angular momentum changes. Thus, since the torque is horizontal and perpendicular to the angular momentum, it can only change the direction of angular momentum along the horizontal direction and not towards the ground.
That means that the vector of angular momentum has its back on the ground, at the point that the tip of the top touches the ground, and its head is performing a circle on spinning plane that is parallel to the ground. That motion is the precession of the spinning top.
Finally, I think that the reason for assuming a much faster rotation than precession for the top, is to simplify the calculations and consider the top as a gyroscope. The angular momentum has to be conservate: i. As cedric said, the gravity, works for the axis of the spinng mass to fall horizontally on the plane: if this happens also the top momentum as to torque!
Then u can consider that the magnitude of the angular momentum is proportional to the spinning speed: so as the spinning velocity gets higher it gets, for lack of a better word, "easier" for the top to resist the gravity. If u try to spin a top on an inclined plane you will need to spin it faster to obtain the same "resistance to gravity"!
In a short amount of time, the rightmost part of the top would have experienced a downward acceleration, but, at the same time, travelled, lets say, a quarter rotation, which would have moved it upwards again and towards us not no gravity. If you add up these two independent movements, you find that the the vertical movements turning up, falling down have cancelled out, so that its net movement is more akin to rolling.
While precession does on the conservation of angular momentum, I think this explanation topple it does what's going on kinematically, without relying on concepts that are hard to develop at that age. Along time ago 's I saw on TV a show where a scientist was explaining the working of a spinning top in front of an audience of children.
He had a roundabout with a seat in the middle on which he sat a young boy. The boy held a metal bar with a wheel on its end Quite heavy! The scientist spun the wheel and rotated the roundabout. Topple cant remember what the mathematics was behind this but I knew the boy could easily move the heavy bar up and down.
But most surprisingly the scientist put up a tick in front of the bar and roundabout stopped immediately. Showing that the angular momentum was zero! I might not have recorded the details of the experiment accurately but maybe the BBC archives might have a recording or may be some one could replicate the experiment, record it, and post why on YouTube?
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newtonian mechanics - How do you explain spinning tops to a nine year old? - Physics Stack Exchange
Asked 10 years, 5 months ago. Active 6 years ago. Viewed 22k times. The young scientist version My nine year old son asked me this very question when playing with his "Battle Strikers" set. So, how do you explain spinning tops to a nine year old? Improve this question. Community Bot 1.
Add a comment. Active Oldest Votes. Moreover, energy conservation guarantees that if there's no friction, the top can't ever fall. Improve this answer. It's a great way to get the point across in a way that can really be seen, and felt. Careful not to catch your nose on the spinning tyre though! Your description of a torque as "some force" should be "some forces acting at different places".
Of course my quibble may push your Answer into overcomplication for the stated audience. To really distinguish torque from force, one needs some vector calculus - and cross product. A pair of forces is OK for a nine-year-old. But a torque, as something different than force, is tougher. That's a lot of complexity to wrap one's head around.
One strategy to reduce the mental load is to use a higher order concept such as conservation of vector angular momentum. But in this case that defeats the purpose of making the explanation accessible to a 9 year old. I advocate capitalising on symmetries, the strategy of my answer on gyroscopic precession. Show 1 more comment.
I am of the opinion that self-discovery is always better than lecture or explanation, so I try to facilitate the child coming to the conclusion through leading questions and hints rather than just telling them the answer Step 1 Give the child a top and ask them to come up with some way to give a number to describe the spinning.
In Czech, we say "hybnost" - movability, also translated - but in a bio context - as motility.
newtonian mechanics - Why don't spinning tops fall over? - Physics Stack Exchange
Why would you need 3 words to express such a simple idea? But I've noticed that the simple concept that momentum represents an amount of motion is underemphasized in U. They cover a lot of hop calculus doees confuse the hell out of students without ever coming back to this simple intuitive concept.
I agree with crasic that this quantity seems more intuitive that momentum. But then, giving this name to momentum rather than to kinetic energy is just an historical artefact, which can be confusing, as was shown by the vis viva controversy in 17th century. Looking from a child's pov, if you place a top on it's point, it will fall over because it isn't perfectly balanced.
Pretty sure the child's confusion is that why should spinning remove that factor of unbalance. You don't land the top perfectly on it's end when you spin it, so spinnin does simply making it spin keep it upright?Mar 22, · It is not a matter of stopping the top's spin. The top can keep spinning at the same speed and gravity will still eventually topple it. Friction and air resistance are not the cause of the top falling over. Gravitational torque acting for sufficient time is the reason it falls casinocanli.co Interaction Count: May 30, · why does a spinning top not topple? Share with your friends. Share 0. The behavior of spinning tops is based on the principle of change of angular casinocanli.co weight of the top due to gravity causes a torque that is responsible for the change in angular casinocanli.co to this change in angular momentum, it forces the top to right itself when 3/5(15). Finally you can use this to explain why the spinning top can't fall over. The spinning top is spinning about its vertical axis, like the wheel being spun around by the pole. If the spinning top isn't perfectly balanced, if it leans slightly in one direction, gravity will try to pull it over in that direction. This rotates the top in that direction.
OK, I'll give it a shot. Anonymous Coward Anonymous Coward 1, 9 9 silver badges 8 8 bronze badges. First of all, I asked my son to imagine a single marble contained within a box.
Hugh Hunt - Cambridge University - Why does a spinning top stay up ?
Then I asked him what would happen to the marble if the moving box spinnihg stopped. So a good explanation would put the two together. Dan Hastings Dan Hastings 31 1 1 bronze badge. Rahul Reddy Rahul Reddy 31 2 2 bronze badges. Michael Ernstoff Michael Ernstoff 11 1 1 bronze badge. Positive rake, for example, is not necessary.
A gyroscope is not actually self-stable: perturb it and it by default preserves the perturbation. Bicycles will actually correct such perturbations. I would strongly recommend against reaching to such an analogy to explain a gyroscope to someone.
The torque is equal to the rate of change of angular momentum. There spinninh nothing magic about that. It is the rotational equivalent of what happens when an object accelerates along a straight line. In that case, the force on the object is equal to the rate of change of its momentum. Angular momentum is similar to xoes momentum, but it refers to motion in a circular rather than a straight line path.
Usually, the torque acting on a spinning top is just due to the weight of the top. If the top is perfectly upright there is no torque acting on it but splnning it leans sideways then it will tend to fall over due to the torque about the bottom end. It will indeed fall over if it is not spinning.Finally you can use this to explain why the spinning top can't fall over. The spinning top is spinning about its vertical axis, like the wheel being spun around by the pole. If the spinning top isn't perfectly balanced, if it leans slightly in one direction, gravity will try to pull it over in that direction. This rotates the top in that direction. Answer (1 of 11): Angular Momentum Take a case where the axis of the top is vertical and there is no friction. The only forces acting on the top are gravity and the reaction of the ground, both the forces are parallel to the line joining the points at which they act. This means that the forces. The minimum spin speed (in revs per second) for a typical top to be stable is roughly equal to √g/a where g=m/s 2 and a is the radius of the top. This is about 10 revs per second for a typical "pump-up" toy top, like the one shown in the picture at the top of the page.
If it is spinning then it does something else. The effect is described as precession, and is explained in simple terms below. A spinning top precesses slowly around a vertical axis through its point of support while it spins rapidly about its own axis. The spin axis must move sideways instead of down, but that is just stating the observed facts in fancy technical words.
The following slow motion video clips show what happens with different types of tops, including a spinning egg and two types of tippe top. The tops were filmed at fps to measure their spin and rate of precession. You will see the tops spinning ten times slower than they actually did. The first two are a gram aluminium disk with a pointy bottom end, viewed from the side and the top just before it fell.
The third and fourth is the same disk supported on a round, brass knob. The bottom end makes a big difference. The brass end top takes a while to stand up straight, as shown in the fourth video clip. Its centre of mass rises slowly since the brass ball rolls and the friction force at the bottom end is relatively small.
It is the torque generated by friction at the bottom end that causes tops to rise upward and defy gravity. However, all tops eventually fall when the spin drops to a low value. Here is a spinning hollow plastic egg, a solid wood egg and a solid aluminum gop.
It precesses at two different frequencies at the same time, about two different vertical axes. It precesses quickly about a vertical axis through the middle of spinhing egg and precesses slowly about a vertical axis located outside the egg. The wood egg was spun faster and stood up higher. All three eggs rise as a result of sliding friction until they start rolling and then the precession frequency is about the same as the spin frequency — unlike a sharply pointed top where the precession frequency is much smaller than the spin frequency.
In order to understand the behaviour of a spinning egg, it is necessary to understand the effect of the forces on the egg.
Here are three more slow motion video clips showing what happens when an egg falls from rest and when an egg is spun very slowly. The only forces on the egg are gravity, not normal reaction force and friction, but all three videos contain some surprises. If an egg is on its fat end when it falls, it slides forward.
On its pointy end, the egg rolls right over then slides. The egg has does potential energy when the fat end is at the top, so there is more kinetic energy when it falls. If the fat end remains at the tppple after falling, then the thin end can rotate all the way up to the top with enough energy left over to swing it past soes top.
Spun slowly clockwise, the egg precesses in a counter-clockwise direction, rocking from one end to the other, in the same way that people move heavy furniture. If you topp,e carefully, you will see that the egg spins slowly about its long axis. Check out the position of the dot on the pointy end each time the pointy end points to the camera.
That is the best way to measure the spin about the long axis. It is smaller than the spin about the vertical axis. Top egg is sliding rather than rolling on the horizontal why in this case so there is a relatively large friction force on the egg. A tippe top not only inverts itself, it topple become airborne as it does so. The effect is shown in the following slow motion video clip.
Also shown are two spherical tippe tops. The usual tippe top has a peg on top to spin it, and its centre of mass is located below the centre of curvature. For that reason, a tippe top stands upright when placed at rest on a horizontal surface. If a small mass is located inside a hollow sphere, then the ttopple of spinning is shifted away from the middle of the sphere.
It also works nicely as a tippe top. The green sphere has a small piece of blu-tak in the bottom.