Answer:
I(x) = 1444×k ×
I(y) = 1444×k ×
I(o) = 3888×k ×
Explanation:
Given data
function = x^2 + y^2 ≤ 36
function = x^2 + y^2 ≤ 6^2
to find out
the moments of inertia Ix, Iy, Io
solution
first we consider the polar coordinate (a,θ)
and polar is directly proportional to a²
so p = k × a²
so that
x = a cosθ
y = a sinθ
dA = adθda
so
I(x) = ∫y²pdA
take limit 0 to 6 for a and o to
for θ
I(x) =
y²p dA
I(x) =
(a sinθ)²(k × a²) adθda
I(x) = k
da ×
(sin²θ)dθ
I(x) = k
da ×
(1-cos2θ)/2 dθ
I(x) = k
×
I(x) = k ×
× (
I(x) = k ×
×
I(x) = 1444×k ×
.....................1
and we can say I(x) = I(y) by the symmetry rule
and here I(o) will be I(x) + I(y) i.e
I(o) = 2 × 1444×k ×
I(o) = 3888×k ×
......................2
The moment of inertia is the rotational analog of mass, and it is given by
the product of mass and the square of the distance from the axis.
- The moment of inertia changes as the position of the weight is changed, which indicates that; statement is incorrect
Reasons:
The weight on each arm that have adjustable positions can be considered as point masses.
The moment of inertia of a point mass is <em>I</em> = m·r²
Where;
m = The mass of the weight
r = The distance (position) from the center to which the weight is adjusted
Therefore;
The moment of inertia, <em>I </em>∝ r²
Which gives;
Doubling the distance from the center of rotation, increases the moment of inertia by factor of 4.
Therefore, the statement contradicts the relationship between the radius of rotation and moment of inertia.
Learn more about moment of inertia here:
brainly.com/question/4454769
C and D are units of length or distance.
A is a measured angle.
B is a unit of angular measurement.
Resistor. The answer is a resistor. They do not transmit electricity.