No, there is no conservation here. The system isn't closed since unbalanced torque and linear forces are supplied by the wall (at B) and the ground where the rolling takes place.
A (presumed solid) cylinder with a known mass and radius has an expressible moment of inertia.
Likewise a (presumed uniform density) stick with known length and mass.
Eww, that's a problem since length of stick is not provided. Is the answer not dependent on stick length then? A long stick will...
Admittedly not a trivial problem. The horizontal force exerted on the cylinder by the stick is not equal to the force exerted on the stick by the wall. The stick gains both momentum (west) and angular momentum (clockwise) as it falls, both reducing the acceleration of the cylinder from the much...
Mutually contradictory statements. I presume there is static friction between the cylinder and the surface upon which it rolls, else it would just start sliding, not rolling.
You have some text, but have not expressed the component forces acting on/by the stick at points A and B, and for that...
Indeed, I forgot the square root part. And I was looking right at it.
The formula you quote (and which I should have quoted) still doesn't take buoyancy into account, as described in my post. Terminal velocity of a helium balloon would be downward, not upward, according to that formula.
Terminal velocity is ((2mg)/(ρAC))
mass, gravity/acceleration, ρ density of fluid, Area and C=drag coefficient
So 6000 psi is about 400 times the density of atmosphere at sea level, so the anvil falls at around 1/400th the speed. This formula doesn't take into account the buoyancy of the...
A ship cannot travel at light speed relative to anything. So say it just goes real fast.
Yes, more time will have elapsed on Earth due to the trip out and back.
The ship has no single inertial frame of reference, so 'the ship's frame of reference' is an accelerated one, and yes, this is true of...
If enough sugar and a slow enough car, it very much does mean that in the frame of the road, he literally travels a path twice as long and twice as fast as the sleeping kid, which is why the kids in the car analogy is terrible.
jbriggs444 expressed it better.
If you mean a large number of clocks all stationary relative to some inertial frame and synced in that frame, then yes, an observer moving relative to that frame and looking at those clocks go by like frames in a movie would see them tick fast by a factor of gamma. He could also watch the...
Infinite energy would entail infinite mass, which would prevent anything from getting into orbit at all.
Perhaps you mean just free energy, in which case you'd have to work out exactly what isn't free and find a solution that makes the most efficient use of those more limited resources.
Any trajectory you put it in will come from the atmosphere. If it isn't moving at escape velocity at the time it exits the atmosphere, it will come back and go through re-entry regardless of trajectory. It cannot reach LEO unassisted.
See? That's a snowman shape, except rotated on its side. Extend it in 3D and it's a snowmanular cylinder.
Sheesh, you guys need to lighten up.
Oh. That wasn't clear from the OP.
If there are n identical cylinders and each has angular momentum of p, then the total angular momentum (be they apart or brought together) is n*p. That or external torque was applied, but you don't indicate that.
So if two of them are brought together, they'll form a sort of spinning...
This seems wrong since the rocket also 'instantaneously' accelerates to its final speed, so it should be viewed as a limit as the burn time decreases to zero, which seems to be the same transfer of momentum to the exhaust regardless of the rate of burn. No matter how short you reduce the burn...
The formula assumes the drain hole is at the rear, as drawn. If it's in the middle, the internal forces are balanced and no such motion results. It needs to be generalized for the position of the hole along (L).
Now consider the system in the frame of the car. It is stationary until the sand...
Dredging this up again. Disclaimer: This is not a speculation. I know very much that the Milne model contradicts empirical measurements. For one, it predicts a linear scalefactor and not the decelerating-then-accelerating one that has been measured.
Yes, from that page. I have a question...
One dam will do. Just build it (the reservoir in particular) upon a sufficiently tall tower. Problem solved.
Have to put a roof on it to keep the water from boiling away. But this seems easier than the two options above, and it doesn't run into the real-estate problem.
Thanks all. That's kind of what I wanted.
Not sure if it's the right thing. The diagram on the right of the wiki page puts the observer at the reference event. It speaks of the cones being the observable universe from that event, where what I was doing was putting the 'bang' at the reference...
I have been using a coordinate system that is anchored on an event (rather than a speed reference) in Minkowskian spacetime. This makes it sort of a special case (no gravity or dark energy, just like special relativity) of the cosmological (or CMB-isotropic) coordinate system used to foliate the...
Didn't read the entire thread, but there are non-inertial frames that do not involve acceleration.
A rotating frame is just one of them. Rotation, like acceleration, is absolute although technically needs a relation to an inertial frame to specify the center of rotation.
The cosmological frame...
OK, since we're getting picking about details, if you do the computation to enough significant digits, a dense object will fall faster as will a more massive object.
@rcgldr hinted at this.
Scenario 1 (difference in mass). Assume m2 masses a significant percentage of Earth, like the moon say...
There are large attractors, for instance (in order of increasing mass and decreasing proximity) Virgo, the Great Attractor, and the Shapley attractor) There is some net rotation about each of these, but no disk to speak of as far as I know.
The universe, if not finite in size, is incapable of...
Plate?
You mean a plane of ecliptic? Yes, if you rotate anything, the material, if it can interact with the other material, will tend to flatten into a disk shape. This is true of silly putty, galaxies, star systems, planets with their moons, although the plane of each might be fairly random...
Yes, relative to the rotating frame of the water/bucket, the water is stationary, and centrifugal force pushes the water to the sides into the parabola shape, and the bucket walls exert an equal an opposite centripetal force that exactly balances it, resulting in no net motion of anything...
Yes, a (quadratic) parabola, but my Latex isn't up to expressing the derivation.
Yes, the water is in equilibrium in that shape due to its inertia, inertia which it isn't going to lose if the system is frictionless. Of course a real bucket needs to spin along with the water to prevent its...
The water assumes the shape due to the motion of the water, not the bucket. There is no force causing the motion outward. That's just the water's own inertia. The water 'wants' to continue in its direction of motion, but the bucket walls (moving or not) exert a centripetal force accelerating...
It is not correct to ground any output. You let it float if you don't care about the 20th bit. Grounding an output wastes energy at best, and burns out your chip at worst. I don't think LS technology will burn out since the fan-out implies an obvious current limit.
In that case, the 1st 19 bits...