Answer:
λ = 451.7 nm
Explanation:
The expression for the constructive interference of the double diffraction experiment is
d sin θ = m λ
let's use trigonometry
tan θ = y / L
how the experiment occurs at very small angles
tan θ = sin θ / cos θ = sin θ
sin θ = y / L
we substitute
d y / L = m λ
λ = 
let's calculate
λ = 
λ = 4.51699 10⁻⁷ m
λ = 4.517 10⁻⁷ m (109 nm / 1m)
λ = 451.7 nm
Ok, assuming "mj" in the question is Megajoules MJ) you need a total amount of rotational kinetic energy in the fly wheel at the beginning of the trip that equals
(2.4e6 J/km)x(300 km)=7.2e8 J
The expression for rotational kinetic energy is
E = (1/2)Iω²
where I is the moment of inertia of the fly wheel and ω is the angular velocity.
So this comes down to finding the value of I that gives the required energy. We know the mass is 101kg. The formula for a solid cylinder's moment of inertia is
I = (1/2)mR²
We want (1/2)Iω² = 7.2e8 J and we know ω is limited to 470 revs/sec. However, ω must be in radians per second so multiply it by 2π to get
ω = 2953.1 rad/s
Now let's use this to solve the energy equation, E = (1/2)Iω², for I:
I = 2(7.2e8 J)/(2953.1 rad/s)² = 165.12 kg·m²
Now find the radius R,
165.12 kg·m² = (1/2)(101)R²,
√(2·165/101) = 1.807m
R = 1.807m
Chemical energy (calories) is converted by your body walking on the surface into mechanical/kinetic energy
