Ph?

To find the moment of inertia of the flywheel, we can use the equation:

I = (mgh - Ffr*d)/ω^2

Where:
I = moment of inertia
m = mass of the weight (18kg)
g = acceleration due to gravity (9.81 m/s^2)
h = distance the weight descends (1.8m)
Ffr = frictional force at the circumference of the spindle (14N)
d = diameter of the spindle (50mm = 0.05m)
ω = angular velocity

First, let's calculate the angular velocity (ω) using the formula:

ω = Δθ/Δt

Where:
Δθ = 2π (since the weight descends once around the spindle)
Δt = 10s

ω = 2π / 10 = 0.628 rad/s

Now, substitute the values into the moment of inertia equation:

I = (18*9.81*1.8 - 14*0.05)/0.628^2
I = (316.404 - 0.7)/0.394384
I = 799.7 kg*m^2

Next, to find the radius of gyration (k), we can use the formula:

I = mk^2

Rearranging for k:

k = sqrt(I/m)

k = sqrt(799.7/981)
k = sqrt(0.815)

Therefore, the radius of gyration is approximately 0.902m.