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The answer to What happens to an astronaut who's floating in a spaceship (in space) when it begins to move? is that we can create g-force just by accelerating. So then why go all the way to create rotating ring?
The ring makes sense for ISS, but why use it for spaceships like the one I see on The Martian. Is there any reason why they can't just accelerate to create gravity?
Constant acceleration requires energy. Our current rocket engines need to use propellant to provide that energy. And there just cannot be enough propellant to generate artificial gravity for any meaningful duration. We would need a new type of space drive to be able to use acceleration that way.
The concept is well known from (science-)fiction (sometimes named "Torchship") and the artifical gravity provided is actually sort of a side effect. The main benefit of a ship able to accelerate at $1G$ fo a long time would be the speed with which it can travel across the Solar System - Mars in two days, Jupiter under one week. But we are not sure if such propulsion system is even possible in reality. Often cited possibilities which might allow it in theory are fusion and antimatter drives.
jkavalik gives the right answer. But to put this in perspective, let me add some numbers.
Let's say, we use a battery of state-of-the-art ion drives to retain a semi-comfortable, Martian level of gravity, of 3.73 m/s2 for a period of 24 hours.
24 h is 86400 seconds. At 3.73 m/s2 this gives 322,272 m/s of delta-V.
Let's use a large number of VASIMIR thrusters, of 12,000 s of specific impulse. Substituting to the Rocket Equation:
$$ \begin{align} \Delta v &= I_\mathrm{sp} g_0 \ln { m_0 \over m_\mathrm f }\\ \ln { m_0 \over m_\mathrm f } &= { \Delta v_0 \over { I_\mathrm{sp} g_0 } }\\ { m_0 \over m_\mathrm f } &= \mathrm e^{ \Delta v_0 \over { I_\mathrm{sp} g_0 } }\\ &= \mathrm e^{ 322272 \over { 12000 \cdot 9.8 } }\\ &= \mathrm e^{2.74}\\ &= 15.48 \end{align}$$
That means, that to maintain gravity of Mars, about third of Earth's, for a period of 24 hours, using ones of the best ion drives we have currently, the craft would need to use 14.48 times its own weight in fuel.
To maintain it over another (earlier) 24 h, it would need 14.48 times the weight of craft plus fuel needed for the second day – about 240 times its own weight. Third day? 3700 times.
So, for 3 days of travel at mild Martian gravity, in a capsule of 10 tons, we'd need to deliver 37 thousand tons of propellant to the orbit.
Basically, we just don't have engines that can accelerate at 1G, or anywhere near that, for more than a few minutes. Not only do we not currently have such engines, we aren't even sure when we will. Nuclear-thermal designs can get at least twice the $I_{SP}$ of chemical rockets, meaning the same amount of thrust can be maintained for twice as long for the same starting mass. (This doesn't mean 1G for twice as long, exactly, but it's fairly close.) Of course, twice as long as "a few minutes" still isn't very good. Project Orion and similar nuclear pulse propulsion designs can achieve much higher $I_{SP}$, but require setting off 1kt nuclear charges repeatedly. Both of these rely on fairly well-proven principles, but we don't have mature designs for them yet, and the current climate toward nuclear reactors and bombs in space is unfavorable, so there's not much serious research.
In particular, the Medusa variant of Orion (using a sail to intercept the nuclear blast along with long tethers reeled in and out to spread its acceleration bursts over time) can likely achieve $I_{SP}$ of close to 100000 s. Consider a mission to Mars at a fairly close approach (<75 million km, with the closest approach being about 40 million km) and a constant 0.3g acceleration/deceleration (to match Mars gravity ahead of time). Per Atomic Rockets, the equation for total time is $t = 2 \sqrt{D/a}$ (which comes out to be about 3.7 days), and the equation for required $\Delta V$ is $\Delta V = 2 \sqrt{D \cdot a}$. Finally, the Tsiolkovsky rocket equation is of course $$\Delta V = v_e \ln {m_0 \over m_1}$$ Assuming a 100 ton dry mass (probably rather low) we can substitute: $$2 \sqrt{D \cdot a} = v_e \ln {m_0 \over m_1}$$ $$m_0 = m_1 \cdot e^{2 / v_e \cdot \sqrt{D \cdot a}}$$ The result is a starting mass of around 270 tons, which means 170 tons of fuel pellets in the form of 1kt nuclear shaped charges, so probably about half highly-enriched plutonium or U-238 and half bomb casing. Needing to acquire close to 100 tons of weapons-grade plutonium for a short trip to Mars is difficult, but not outright impossible. Accepting a lower gravity of, say, 0.1g the whole time (which may or may not be enough for comfort, but over a short duration, in this case about 6.3 days, is not going to affect bone density much) would cut the required propellant mass in half.
Other designs either don't have enough thrust to create decent gravity, or don't have enough $I_{SP}$ for continuous running during a voyage, or are very speculative. (Antimatter rockets, say, are a very long ways from being practical.)
Acceleration costs the energy. Let's ignore everything else - suppose we are in free space, there is no gravity, no drag, no other motions. then energy $E$ needed to gain velocity $v$ is $E=1/2 mv^2$.
If you want to maintain given acceleration $g$ you will ned a power source that can provide output of $P(t)=mgv(t)$ (I've just derived the energy by time) all the time.
If we use rotation to get feeling of gravity we just need to rotate the ring. The "gravity" will be $g=\omega^2 r$ and the energy needed to accomplish that is $E=1/2J\omega^2=\frac{J\cdot g}{2r}$.
No matter how the engines would work, how effective they would be; the gravity by rotation will be more effective that gravity by propulsion.
