# Tether rotation device in space problem

• nhmllr
In summary, a spaceborne energy storage device with two equal masses connected by a tether and rotating about their center of mass can store additional energy by reeling in the tether. This is achieved without the application of external forces. The kinetic energy of the device initially is E and it rotates at angular velocity ω. After adding energy, the device rotates at angular velocity 2ω. The new kinetic energy of the device is 2E. The conservation of angular momentum, Mωr2, remains constant throughout the process, with the product of angular velocity and radius, ωr, also remaining constant.
nhmllr

## Homework Statement

A spaceborne energy storage device consists of two equal masses connected by a tether and rotating about their center of mass. Additional energy is stored by reeling in the tether; no external forces are applied. Initially the device has kinetic energy E and rotates at angular velocity ω. Energy is added until the device rotates at angular velocity . What is the new kinetic energy of the device?

(The answer is 2E but I don't see how)

## Homework Equations

kinetic energy = 1/2*mv^2
momentum = mv = mωr
initial momentum = final momentum

## The Attempt at a Solution

I don't see how this "energy storage" works. If I real the tether in, the radius r of the device decreases but the angular velocity ω of the device increases because of the conservation of momentum. The kinetic energy of the device is 1/2*m(ωr)^2, but the quantity ωr does not change. So I don't see how the potential energy of the device can be converted.

ω and r both change when the device is reeled in. Call them ω1 and r1. The product of angular velocity and radius is what remains constant, so that ω1*r1 = ω*r.

gneill said:
ω and r both change when the device is reeled in. Call them ω1 and r1. The product of angular velocity and radius is what remains constant, so that ω1*r1 = ω*r.

Right. If ω1*r1 = ω*r, then the kinetic energy stays the same. I still don't understand what the problem is talking about with the "stored energy," because reeling in the tether doesn't affect the energy.

Ah. Sorry, I misspoke. Angular momentum is conserved, so it's Mωr2 that remains constant. Since M is the same in both cases, ωr2 is what you need to worry about. The square makes a difference

It seems that the concept of this spaceborne energy storage device is based on the conservation of angular momentum. As the tether is reeled in, the radius of the device decreases, causing an increase in angular velocity. This increase in angular velocity results in an increase in kinetic energy, which is represented by the equation 1/2*m(ωr)^2. Since the device initially has kinetic energy E and rotates at angular velocity ω, the equation would be 1/2*m(ωr)^2 = E. When the device rotates at angular velocity 2ω, the new kinetic energy would be 1/2*m(2ωr)^2 = 4E. This shows that the new kinetic energy is indeed 2E, as stated in the problem. The potential energy is not being converted, but rather the kinetic energy is increasing due to the change in angular velocity.

## 1. What is a tether rotation device in space problem?

A tether rotation device in space problem refers to the issue of maintaining the stability and control of a rotating tether in space. This device is used to generate artificial gravity in space habitats or spacecraft. However, problems may arise due to factors such as tether material strength, control mechanisms, and external forces.

## 2. How does a tether rotation device work?

A tether rotation device typically consists of a long, flexible tether connected to a spacecraft at one end and a counterweight at the other. The spacecraft spins around its axis, creating centrifugal force that pulls the tether taut and creates artificial gravity. The counterweight helps to balance the system and keep it stable.

## 3. What are some challenges of using a tether rotation device in space?

There are several challenges associated with using a tether rotation device in space. These include the difficulty of maintaining a constant rotational speed, potential damage or breakage of the tether, and the effects of external forces such as solar wind and atmospheric drag. Additionally, controlling the rotation and orientation of the spacecraft can be complex and requires precise maneuvers.

## 4. Are there any solutions to the tether rotation device problem?

Yes, there are several proposed solutions to the tether rotation device problem. These include using stronger and more durable tether materials, implementing advanced control systems, and utilizing thrusters or other external forces to maintain stability. Extensive research and testing are also being conducted to improve the design and functionality of tether rotation devices.

## 5. What are the potential benefits of a tether rotation device in space?

The main benefit of a tether rotation device in space is the creation of artificial gravity, which can have numerous advantages for long-term space missions and human habitation. This includes reducing the negative effects of microgravity on the human body, enabling more efficient and comfortable living conditions, and facilitating experiments and activities that require gravity. Tether rotation devices also have the potential to enable new space propulsion techniques and reduce the need for fuel.

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