Energy (work) needed to spin up and maintain a flywheel?

Question

What energy (work) is needed to spin up and then maintain a 3.5" diameter flywheel weighing 680 grs turning at 120 rpm on a horizontal plane?

The flywheel is comprised of flywheel plate and a stationary sun gear, weighing 200 grs. Attached to the flywheel are 4 planetary gears engaging the sun gear each weighing 120 grs. (Should you need the following info, the sun gear is 2" in dia and the planetary gears are 1" in dia. - assume no friction.)

Many thanks

Answer 1

I believe it is not just a fly wheel spinning a system is in motion.

The flywheel is spinning at 120rpm
The sun gear is spinning at 120 rpm
each planetary gear is spinning at ( 2:1 ) 240rpm

Since there is no resistance once spinned no additional energy will be required to maintain the the system in rotation.

Ke - kinetic energy = K1+K2+4(K3)

In general K=.5 I w^2
I - moment of inertia (rotational mass)
w – angular velocity =2 pi (RPM) 60 (radians/sec)

I= .5mR^2
M – mass (kg)
R – radius (meters)

K1=.5 I1 w1^2
K2=.5 I2 w1^2 (same as w1=w2)
K3=.5 (4) I3 w1^2 (w3=2w1)
K3=2 I3 w1^2

Kt= .5 I1 w1^2 + .5 I2 w1^2 + 4( 2 I3 w1^2)
Kt= (.5 I1 + .5 I2 + 8 I3 )w1^2
Kt = .5(I1 + I2 + 16 I3)w1^2
Kt= 0.5(.5m1 R1^2 +.5m2R2^2 + 16 .5 m3 R3^2)w1^2
Kt=.25 (m1 R1^2 + m2R2^2 + 16 m3 R3^2)w1^2
Now just do the math