what is the moment of interia of a solid cylinder of radius R=0.0950m thickness t=0.015m total mass M=3.565kg? show your work
Moment of Ineria= 1/2 MR^2 = 1/2 (3.565kg)(0.0950m)^2= 0.016 kg.m^2
The moment of inertia of a solid cylinder or disc is (1/2) M R^2, and does not depend upon the thickness.
The moment of inertia, I, of a solid cylinder can be calculated using the formula:
I = (1/2) * M * R^2
where M is the mass of the cylinder and R is the radius. To calculate I, we need to first find the mass of the cylinder.
Given:
Radius, R = 0.0950 m
Thickness, t = 0.015 m
Total mass, M = 3.565 kg
To find the mass of the cylinder, we need to consider the volume of the cylinder.
The volume, V, of a cylinder can be calculated using the formula:
V = π * R^2 * h
where h is the height of the cylinder. In this case, the height is the thickness, t.
V = π * (0.0950 m)^2 * 0.015 m
V = 0.000212 m^3
Now, we can find the density, ρ, of the cylinder, which is the mass per unit volume.
ρ = M / V
ρ = 3.565 kg / 0.000212 m^3
ρ = 16,809.43 kg/m^3
Finally, we can calculate the mass using the formula:
M = ρ * V
M = 16,809.43 kg/m^3 * 0.000212 m^3
M = 3.565 kg
Now that we have the mass, we can calculate the moment of inertia using the formula:
I = (1/2) * M * R^2
I = (1/2) * 3.565 kg * (0.0950 m)^2
Now, plugging in the values:
I = (1/2) * 3.565 kg * (0.0950 m)^2
I = 0.033984 kg*m^2
Therefore, the moment of inertia of the solid cylinder is 0.033984 kg*m^2.
To find the moment of inertia of a solid cylinder, you can use the formula:
I = (1/2) * M * R^2
Where:
I is the moment of inertia
M is the mass of the cylinder
R is the radius of the cylinder
Given values:
M = 3.565 kg
R = 0.0950 m
Now, let's substitute these values into the formula:
I = (1/2) * (3.565 kg) * (0.0950 m)^2
Calculating the equation:
I = (1/2) * (3.565) * (0.0950^2)
I = (1/2) * 3.565 * 0.009025
I = 0.0160990625 kg·m²
Therefore, the moment of inertia of the solid cylinder is approximately 0.0161 kg·m².