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1. 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.
2. 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)
3. The Attempt at a Solution
A. A= 1/2 pi R^2 =8pi
B.
C.
D.
E.
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.
2. 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)
3. The Attempt at a Solution
A. A= 1/2 pi R^2 =8pi
B.
C.
D.
E.
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