Where does energy go?

i have a device where a spinning mass switches from a radius of 100 m to a radius of 1m by means of gearing, going the mass of 1 kg at a speed of 100 m/s

lets consider it frictionless

in order to reduce the radius i have to aply a work, the energy to aply that work comes from the 100 m/s of the mass because theres no other energy in the system

so when the ball has a radius of 1 m it has a lower speed having lost kinetic energy

my question is if the device is frictionles where has this kinetic energy gone to?

Galileo
Homework Helper
I`m not sure what you mean exactly, but when you reduce the radius of the spinning object it will start to spin faster (conservation of angular momentum), so it picks up rotational kinetic energy (equal to the work you performed to bring the mass closer to the axis of rotation).

a ball is geared to an axe in such way that the radius decreases constantly as it spins

would it be correct to say that because of conservation of momentum if when it has a radius of 100 m has a speed of 100m/s when it has a radius of 1 m still has a speed of 100 m/s?

Galileo
Homework Helper
No, since the initial angular momentum is rmv=(100)(1)(100) = 10.000 kg m^2/s, when the ball

spins with a radius of 1m, the angular momentum will be still be 10.000 kgm^2/s =(1)(1)(v). So v=10.000 m/s.

If you pull in the ball radially, the torque on the ball will be zero, so its angular momentum is conserved.
Linear momentum obviously is not, since the ball rotates (there's a centripetal force acting on it).

Last edited:
you are wrong its been accepted by a mod here that speed is kept at 100 m/s however radius, this case is called a tetherball

Doc Al
Mentor
aviator said:
you are wrong its been accepted by a mod here that speed is kept at 100 m/s however radius, this case is called a tetherball
As usual, you have no idea what you are talking about. You must specify whether you are actively reeling in the cable (this is what Galileo assumed in his response to your vaguely worded question) or just letting it wrap around a pole (like the tetherball case). These are different scenarios with different answers.

Stick to one scenario and get it straight. Stop posting the same thing over and over.