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.

Please help

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

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.

To calculate the mass of a flywheel, you need to know its density, diameter, and width. Here are the steps to determine the mass:

Step 1: Convert the diameter and width measurements to meters.
- The given diameter is 760 mm. Convert it to meters by dividing it by 1000.
Diameter = 760 mm ÷ 1000 = 0.76 meters
- The given width is 180 mm. Convert it to meters in the same way.
Width = 180 mm ÷ 1000 = 0.18 meters

Step 2: Calculate the volume of the flywheel.
- The volume of a cylinder (which the flywheel resembles) is V = π * r^2 * h, where r is the radius and h is the height (in this case, the width).
- Since the diameter is given, calculate the radius by dividing it by 2.
Radius = 0.76 meters ÷ 2 = 0.38 meters
- Now, substitute the values into the formula:
Volume = π * (0.38 meters)^2 * 0.18 meters

Step 3: Calculate the mass of the flywheel.
- Mass can be calculated by multiplying the volume by the given density:
Mass = Volume * Density

Now, let's put all the values into the formula to find the mass:
- Density = 7800 kg/m³ (given)
- Volume = π * (0.38 meters)^2 * 0.18 meters (calculated in step 2)

First, calculate the volume using the given values:
Volume = π * (0.38 meters)^2 * 0.18 meters
Next, multiply the volume by the density to find the mass:
Mass = Volume * Density

By following these steps and substituting the values, you should be able to calculate the mass of the flywheel.