How do i work out the mass of a flywheel. I am given the density as 7800kg/m3, a 760mm diameter and a 180mm width.

Question

Please help

Answer 1

ρ = density

ρ = 7800 kg /m³

1 m = 1000 mm

1 m³ = ( 1000 )³ = ( 10³ )³ = 10⁹ mm³

ρ = 7800 / 10⁹ = 7.8 ∙ 10³ / 10⁹ = 7.8 / 10⁶ kg / mm³

A = Area

A = d² ∙ π / 4

V = Volume

V = w ∙ A

V = w ∙ d² ∙ π / 4

m = ρ ∙ V

m = ρ ∙ w ∙ d² ∙ π / 4

m = 7.8 / 10⁶ ∙ 180 ∙ 760² ∙ π / 4

m = 7.8 / 10⁶ ∙ 180 ∙ ( 7.6 ∙ 100 )² ∙ π / 4

m = 7.8 / 10⁶ ∙ 180 ∙ ( 7.6 ∙ 10² )² ∙ π / 4

m = 7.8 / 10⁶ ∙ 180 ∙ 7.6² ∙ 10⁴ ∙ π / 4

m = 7.8 / 10² ∙ 180 ∙ 7.6² ∙ π / 4

m = 7.8 / 10² ∙ 180 ∙ 57.76 ∙ π / 4

m = 7.8 ∙ 180 ∙ 57.76 ∙ π / 10² ∙ 4

m = 81095.04 ∙ π / 10² ∙ 4

m = ( 81095.04 / 4 ) ∙ π / 10²

m = 20273.76 ∙ π / 10²

m = 2.027376 ∙ 10⁴ ∙ π / 10²

m = 2.027376 ∙ 10² ∙ π

m = 202.7376 ∙ 3.14159

m = 636.918416784 kg

m ≈ 637 kg

OR

ρ = 7800 kg / m³

d = 760 mm = 0.76 m

w = 180 mm = 0.18 m

m = ρ ∙ V

m = ρ ∙ w ∙ d² ∙ π / 4

m = 7800 ∙ 0.18 ∙ 0.76² ∙ π / 4

m = 7800 ∙ 0.18 ∙ 0.5776 ∙ π / 4

m = 810.9504 ∙ π / 4

m = ( 810.9504 / 4 ) ∙ π

m = 202.7376 ∙ π

m = 202.7376 ∙ 3.14159

m = 636.918416784 kg

m ≈ 637 kg

Answer 2

V = pi*r^2*W = 3.14 * 0.38^2 * 0.18 = 0.0816 m^3.

Mass = 7800kg/m^3 * 0.0816m^3 = 637 kg.