So sad Please Register or Log in to view the hidden image! A specially for you again: Base on trivial case of problem, the figure 4 shows a model for experiment where wheels and solid block covers by another platforms on wheels. Please Register or Log in to view the hidden image! The wheel1_1 and wheel1_2 connect with cover by axis. For easies calculation, all doted elements, platforms and spring are weightless. Let's assume the law of momentum conservation always works in simplest form. In this case, the forces on both sides of spring are equal by value and induce translational motions for solid block and rolling objects on both platforms. However, which force induce rotational motion for rolling objects on one platform? The solid block doesn't conduct rotational motion on other platform. On one platform, the rolling objects rotate on opposite direction for each other and have same angular momentum by value and opposite direction. However, need a force to induce this rotation. The asymmetrical force cannot exist during interaction. Therefore, the assumption where law of momentum conservation exist in simple form during complex interaction is wrong.
Why do you insist? All you are doing is to make yourself look quite clueless, and that is putting things as nicely as I can.
DH, I'm smiling Please Register or Log in to view the hidden image! OK. Let's get to your solution problem. Your equations (7) and (8). The force for translational motion Fu should not be the same as force which make a rotation of this wheel. Why? The projection force for rotation motion is depend how object rolling on platform, but not how object do translational motion by platform. Other words Here's no equivalence of these forces and sum of them will be net force which spring applied to platforms with rolling objects. You may get any standards problems for rolling objects on surface and you will see two forces. Where one of them is responsible for translational motion and another for rotational motion. Sum of them is a net force which will be apply to object. I hope it helps.
You're wrong. A force can simultaneously cause translational and rotational motion. This is a FACT, one that derives from either Newton's laws of motion (in which the conservation laws are derived relationships) or from the conservation laws (in which Newton's laws of motion are derived relationships). You can rail against this fact as much as you wish, but all your wishing / all your intentional ignorance will not change this fact. It will make you look stupid, however.
You mean if integrate this force then it's possible get free angular momentum from nowhere? I don't think so. Visa versa. The integration of symmetrical interaction will give a law of conservation. These laws the consequences of symmetrical interaction. You can't reverse it like physical meaning. Just like math equation. I'm completely disagree to get momentums and energies from nowhere. Unfortunately, the modern classical mechanic do this every time when need to keep simplifications of law of momentum conservations. This is wrong. The symmetrical interaction cases with simple symmetrical consequences as law of momentum conservations in simple form cannot describe the complex asymmetrical interactions. It's impossible induce motion without force. However, the classical mechanic do this all the time in complex interactions calculations. How is it possible to prove? The experiment! I made my own, but it's not very accurate. For clear results need a lab environment. That's because,I'm Looking For Special Research Group Who can help? Anyone?
ABV: The force that induces rotation here is presumably a friction force between the rope joined to the spring and the rotating wheels.
Of course not. A force must necessarily cause translation via \(\vec F= \frac{d\vec p}{dt}\) to conserve linear momentum and must also cause rotation via \(\vec r \times \vec F = \frac{d (\vec r \times \vec p)}{dt}\) to conserve angular momentum. This is a standard derivation in the classical mechanics course that most physics majors take as sophomores or juniors. Pick up any text on classical mechanics. The derivation will be very close to the front of the book.
The experiment for this physics problem: http://knol.google.com/k/alex-belov/the-wheels/1xmqm1l0s4ys/18#The_Experiment Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image!
The experiment for this physics problem: http://knol.google.com/k/alex-belov/the-wheels/1xmqm1l0s4ys/18#The_Experiment Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image! The video http://www.youtube.com/watch?v=FjYsQnaocws&feature=player_embedded
1 Your equipment is of low precision 2 There is an asymmetry in the mass transfer and the masses measured are not equal to the relevant masses throughout the experiment 3 You fail to control for the friction of the platforms 4 You failed to repeat your experiment to control for the slope of the tabletop 5 The positions of the laser pointers does not reflect the center of mass, which would be important if the accuracy were high 6 At the end of the video, the right laser pointer mark moves backwards, which suggests that your data is of low precision 7 No one believes you are intellectually honest 8 A better experiment in every way can be done with maglev tracks or a 1-d pneumatic levitation track ala "air hockey" or ballistic pendulums
Really? How low? The statement of nothing. I gave mass of both platforms with all parts. Really? I use standard rollers. You think they have a bid deviation? All them was oiled and checked for now long they rotate. Mostly same result. What do you mean failed to repeat? You were there? Really? You think the cart change own dimension during the experiment? Please Register or Log in to view the hidden image! These carts don't have relativistic velocities Please Register or Log in to view the hidden image! If you check again, you'l see both carts a little roll back after stop. It means carts is to sensitive to balance of wheels. You are all of us. Congratulations! Please, take a doctor Please Register or Log in to view the hidden image! Or, please, talk about yourself only. Whatever you like. I'm looking forward for your experiment. If you'd like repeat mine, I'll sponsor you.