The variable y is directly proportional to the variable x. If y = 12 when x = 14, what is the value of x when y = 247
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The moment of inertia about the y-axis of the thin semicircular region of constant density is given below.
Any item that can be turned has rotational inertia as a quality. It's a scalar value that indicates how complex it is to adjust an object's rotational velocity around a certain axis.
Then the moment of inertia about the y-axis of the thin semicircular region of constant density will be
x = r cos θ
y = r sin θ
dA = r dr dθ
Then the moment of inertia about the x-axis will be
On integration, we have
Then the moment of inertia about the y-axis will be
On integration, we have
Then the moment of inertia about O will be
More about the rotational inertia link is given below.
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