How Much Energy Can Be Extracted from a Rotating Disk?

[aladinlamp]

As you can see, solid disk is rotating at steady angular speed, without any external force beeing applied.

If i stop it gradualy within 60 second, by applying some linear load, how many kWh can i extract from this moving object?

 

[mfb]

At most the total kinetic energy. You just have to convert J to kWh.

 

[aladinlamp]

At most the total kinetic energy. You just have to convert J to kWh.

If i double angular speed,it doubles angular momentum but but why it quadruples Kinetic energy ?

If i apply load in this case and slow down the wheel by 50%, it looses 75% of kinetic energy, so i think total amount of J which i can extract is more complex to determine or am i missing something?

 

[A.T.]

If i double angular speed,it doubles angular momentum but but why it quadruples Kinetic energy ?

Because of how they are defined.

 

[aladinlamp]

ok so in real life, to stop wheel in 60 seconds i need some load,
to stop wheel with double speed in 60 seconds, do i need double load or quadruple load ?

i would say , i need just double load

so what does this KE represent in real life?

 

[A.T.]

so what does this KE represent in real life?

This:

how many kWh can i extract from this moving object?

 

[aladinlamp]

my point is, to accelerate wheel from zero to some speed it takes 1 unit of J

to double the speed it takes another 1 unit of J

so 2 unit of J total, linear relationship, when it comes to power inputbut somehow power output, KE is not linear but exponencial ?

 

[A.T.]

my point is, to accelerate wheel from zero to some speed it takes 1 unit of J

to double the speed it takes another 1 unit of J

No, it takes additional 3J to double the speed that was achieved by 1J.

 

[aladinlamp]

if i set torque to fixed value, to accelarate from zero to some speed it takes 1 unit of time, to accelarate to double speed from zero with same torque, it takes 2 units of time

so i see pretty linear input, not 1J vs 3J as you said

 

[A.T.]

so i see pretty linear input,

Input of what?

 

[aladinlamp]

torque * time
or
force * time

 

[A.T.]

torque * time

Is that energy?

 

[aladinlamp]

no its, not

but how do you calculate it in this case,

In rotational systems, power is the product of the torque τ and angular velocity ω,

this is linear relationship, just tell me how did you get your exponencial

is it sum of energies from zero to some speed vs sum of energies from some speed to double speed?

 

[A.T.]

but how do you calculate it in this case,

http://hyperphysics.phy-astr.gsu.edu/hbase/rke.html

 

[aladinlamp]

ok so according to this

if i rotate the wheel with some electric motor and measure electricity consumption
from zero to speed x ,it will take let's say 10 seconds and i will use let's say 1 kwh

during another 10 seconds i accelerate from x to 2x, and use additional 3 kwh ?

is this correct according to facts above?

 

[A.T.]

ok so according to this

if i rotate the wheel with some electric motor and measure electricity consumption
from zero to speed x ,it will take let's say 10 seconds and i will use let's say 1 kwh

during another 10 seconds i accelerate from x to 2x, and use additional 3 kwh ?

is this correct according to facts above?

Assuming 100% efficiency, yes.