- #1

nhmllr

- 185

- 1

## 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

*2ω*. 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.