A thin steel plate is in the shape of a half circle

[Melina]

Homework Statement

The half thin steel plate has a radius of 4 meters and a surface density of (3+r) kg/m^2, where r is the radial distance from the origin. Using calculus, find:
A. its area
B. its mass
C. Its center of mass with respect to the origin shown,
D. It's rotational inertia about the j axis
E. Its rotational inertia about an axis parallel to the j axis and passing through the center of mass.

Homework Equations

d=v0 t + (1/2)at^2
a=v^2 / r
v=v0 + at
v=dx/dt
a= dv/dt
σ = dm/dA φ = dm/dV
I = r^2 dm Ix+Iy = Iz
I = ICM + m k^2 (CM:center of mass subscript)
Discrete masses:
xCM = ∑mixi (CM:center of mass subscript)
i
-----------
∑mi
i
continuous mass distributions:
xCM = 1/M ∫x dm (CM:center of mass subscript)

The Attempt at a Solution

A. A= 1/2 pi R^2 =8pi
B.
C.
D.
E.

 

[Nathanael]

Part A is right. Please show your attempts for the other parts if you want help.