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## 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.