# Final speed of a rotating spaceship

• Susanne217
In summary, the conversation discusses the calculation of the extra speed achieved by an engine burst on a rotating ship in the movie 2010 and the formula used for this calculation. The answer is supposed to be 24400 km/h according to the book, but the reader is struggling to arrive at this answer using the formula F = 1/2 * m * v_f^2 - 1/2 * m * v_i^2.

## Homework Statement

Lets imagine that in the movie 2010. The Discovery is rotating then they find it. Every time the ship reaches a speed in the circular motion of 24000 km/h the engine gives a burst of energy. Which amounts to 20 kN. The mass of the Discovery is 30.000 kg. The time from the engine gives a burst amounted to the above size to the ships engine going to sleep is 3 minutes.
How do I calculate the extra speed v_final which is achieved by the engine burst after the three minutes. Necletecting all other forces?

Is there a specific formula?

According to my book. the answer is suppsed to be 24400 km/h.

I have to tried to the formula

$$F = 1/2 \cdot m v_f^2 - 1/2 \cdot m v_i^2$$

But using that formula I arrive at v_final = v_initial.

What am I doing wrong?

Sincerely
Susanne

Your scenario has the information: acceleration force (20 kN), mass (30 ton) and time (180 seconds); and you want to calculate the resulting change of speed. A way forward could be to figure out how force and mass relates to acceleration and how (constant) acceleration relates to change in speed.

## What is the final speed of a rotating spaceship?

The final speed of a rotating spaceship depends on a few factors such as the initial speed, the rate of rotation, and the amount of time the spaceship has been rotating. It also depends on whether the spaceship is accelerating or decelerating during the rotation. In general, the final speed of a rotating spaceship can range from 0 to very high speeds, depending on these factors.

## How does the rate of rotation affect the final speed of a rotating spaceship?

The rate of rotation can greatly affect the final speed of a rotating spaceship. The faster the spaceship is rotating, the greater the centripetal force acting on it, and therefore the greater the final speed will be. This is why spacecrafts that need to reach high speeds often use rotating components in their design.

## What is the difference between the final speed and the tangential speed of a rotating spaceship?

The final speed of a rotating spaceship is the total speed at which it is moving, taking into account both the tangential speed and the centripetal speed. The tangential speed is the component of the final speed that is in a straight line tangent to the circle of rotation. In other words, the tangential speed is the speed at which the spaceship is moving in a straight line, while the final speed takes into account the curved path of the rotation.

## Can the final speed of a rotating spaceship be greater than the speed of light?

No, according to the theory of relativity, the speed of light is the maximum speed at which anything in the universe can travel. This means that even if a rotating spaceship were to reach incredibly high speeds, it would still not be able to exceed the speed of light. However, the final speed of a rotating spaceship can still be significant and can have a significant impact on the spaceship's overall performance.

## How does the final speed of a rotating spaceship affect its stability?

The final speed of a rotating spaceship plays a crucial role in its stability. If the speed is too low, the spaceship may not have enough centripetal force to maintain its rotation and could potentially crash or spin out of control. On the other hand, if the final speed is too high, the spaceship could experience excessive centrifugal force and may become unstable. Finding the right balance of final speed is important for ensuring the stability and safety of a rotating spaceship.

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