In: Civil Engineering

A quarter circle of radius 100 mm lies on Quadrant II of a
coordinate plane with

reference radius at the origin. A rectangle is attached to the
quarter circle at Quadrant I

with base at the x-axis of width equal to 25 mm and height same as
the radius of the

quarter circle. Another rectangle with inverse dimension as the
previous is attached to the

quarter circle at Quadrant III.

a. What is the moment of inertia (m4) of the composite area with
respect to the x-axis at point O?

b. What is the moment of inertia (m4) of the composite area with
respect to the y-axis at point O?

c. What is the polar moment of inertia (m4) of the composite
area?

d. What is the centroidal moment of inertia (m4) of the composite
area?

e. What is the radius of gyration (mm) of the composite area with
respect to its

centroid?

A quarter circle of radius 227 mm lies on Quadrant II of a
coordinate plane with reference radius at the origin. A rectangle
is attached to the quarter circle at Quadrant I with base at the
x-axis of width equal to 45.6 mm and height same as the radius of
the quarter circle. Another rectangle with inverse dimension as the
previous is attached to the quarter circle at Quadrant III.
a. What is the moment of inertia (m4) of the...

Acircular ring of radius ?lies in the ??plane and is centered on
the origin. The half on the positive ?side is uniformly charged
with a charge +?while the half on the negative ?side is uniformly
charged with a total charge −?.
a..Draw a diagram of the charge distribution and without doing
any math, determinethe direction of the total electric field at the
origin
. b.Calculate the ?component of the electric field at the origin
by integrating the charged ring.
i.Draw...

A circle with a radius of 0.3 meters is placed in the x-y plane
in a magnetic field directed in the -z direction. It is wound once
and its resistance is 8 Ohms. The initial magnetic field is 0.5
Tesla. The magnetic field is then changed in 0.7 s and the average
induced current is 0.05 amps running counter-clockwise. First, find
the final magnetic field to needed to induce this average
current.
Then, the magnetic field (still in the -z...

A circular area with a radius of 6.60 cmcm lies in the xx-yy
plane.
A) What is the magnitude of the magnetic flux through this
circle due to a uniform magnetic field BB = 0.211 TT that points in
the +z+z direction?
Express your answer in webers.
B) What is the magnitude of the magnetic flux through this
circle due to a uniform magnetic field BB = 0.211 TT that points at
an angle of 52.7 ∘∘ from the +z+z...

1) A circle with a radius of 0.3 meters is placed in the x-y
plane in a magnetic field directed in the -z direction. It is wound
once and its resistance is 6 Ohms. The initial magnetic field is
0.8 Tesla. The magnetic field is then changed in 0.6 s and the
average induced current is 0.04 amps running counter-clockwise.
First, find the final magnetic field to needed to induce this
average current.
Then, the magnetic field (still in the...

1) A circle with a radius of 0.3 meters is placed in the x-y
plane in a magnetic field directed in the -z direction. It is wound
once and its resistance is 7 Ohms. The initial magnetic field is
0.6 Tesla. The magnetic field is then changed in 0.7 s and the
average induced current is 0.05 amps running counter-clockwise.
First, find the final magnetic field to needed to induce this
average current.
Then, the magnetic field (still in the...

A four-turn circular wire coil of radius 0.550 m lies in a plane
perpendicular to a uniform magnetic field of magnitude 0.355 T. If
the wire is reshaped from a four-turn circle to a two-turn circle
in 0.128 s (while remaining in the same plane), what is the average
induced emf in the wire during this time?

Consider a wire of uniform density and mass M shaped into a
quarter circle of radius R.The wire is located in the xy plane,
with the origin at the focus of the quarter circle (i.e at the
center of the circle of which the wire is part). Choose the x axis
parallel to the line that connects the endpoints of the wire, so
that the y-z plane is a plane of reflection symmetry for the wire.
This means that the...

Find a path that traces the circle in the plane y=0 with radius
r=2 and center (2,0,−2) with constant speed 12.
r1(s)=〈 , , 〉
Find a vector function that represents the curve of intersection
of the paraboloid z=7x^2+5y^2 and the cylinder y=6x^2. Use the
variable t for the parameter.
r(t)=〈t, , 〉
Need help with Calculus III

Let C be the boundary of the quarter circle with radius 1,
oriented counterclockwise (Figure 1). Evaluate H C(ex + y2) dx +
(ey + x2) dy

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