Question

Calculate the rotational inertia about the x-axis of a solid of revolution y = x^2 about the y-axis with a height of 4 m. Assume the solid is made of aluminum (? = 2.7 g/cm3)

Answer #1

Find the mass of a solid of revolution y = x^2 about the y-axis
with a height of 4 m. Assume the
solid is made of aluminum (? = 2.7 g/cm3)

Find the volume of a solid of revolution that is formed by
rotating about the y-axis with the curve y = x4-
x2.
Use Riemann sum to calculate.

A
solid of revolution is generated by rotating the region between the
y-axis and the graphs of g(y)=y2+2y+2, y=−3, and y=0 about the
y-axis. Using the disk method, what is the volume of the
solid?

Find the volume of the solid of revolution formed by rotating
the region about the y-axis bounded by y2 = x and x =
2y.

Find the volume of the solid of revolution formed by rotating
about the x-axis the region bounded by the curves
f(x)=4x^2
y=0
x=1
x=2
___
What is the volume in cubic units? (Exact answer using
π as needed)

The rotational inertia I of any given body of mass
M about any given axis is equal to the rotational inertia
of an equivalent hoop about that axis, if the hoop has the
same mass M and a radius k given by
The radius k of the equivalent hoop is called the
radius of gyration of the given body. Using this formula,
find the radius of gyration of (a) a cylinder of
radius 3.72 m, (b) a thin spherical shell...

Calculate the rotational inertia of a meter stick with mass
m=0.56 kg about an axis perpendicular to set stick and located at
the 20 cm mark. (Treat the stick as a thin rod).

2) Find the moment of inertia and the radius of gyration of:
y=x2 , X=0 and y=9 about the y-axis. Assume ? = 5. (Hint: This is
rotating a flat plate, like a flag. Not a volume as in #3 and #4)
ANSWER- Iy=162 R=Sq.Root(162/18)
3) Find the moment of inertia and the radius of gyration of the
solid formed by rotating y=3x, y=0 and x=2 about the y-axis. Assume
? = 15. Answer- Iy= 176pi R= Sq.root(276pi/240pi) Need the...

Find the surface area of revolution for y = 2
√x over (2,4), about the x-axis.

Calculate the rotational inertia of a meter stick, with mass
0.633 kg, about an axis perpendicular to the stick and located at
the 27.4 cm mark. (Treat the stick as a thin rod.)

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