Question

Find the center of mass of a semicircular metal sheet of radius
R.

Answer #1

A neutral metal can of radius R = 3.50 cm and mass m = 2.00 g is
rolling without slipping on a level surface as a positively charged
rod is kept at a distance 4.00 cm from the center of the can. If
the can accelerates at 0.227 cm/s2 , how many electrons are in the
can?

Find the moment of inertia of a uniform hollow sphere of mass M,
inner radius r, and outer radius R > r, about an axis through
the center of mass. Consider your answer for the cases r → 0 and r
→ R. Does the result reduce correctly? Explain.

(1). The mass density of a semicircular wire of radius a varies
directly with the distance from the diameter that joins the two
endpoints of the wire. Find the mass equation 人(x,y)
(2) Let say now the density varies directly as the cube of the
distance from the line that divided the wire in half vertically.
Fin the mass equation 人(x,y)

You have a solid metal cylinder of mass M, with a radius of
R. What is its moment of inertia?
(1/2)MR2
MR2
(2/3)MR2
(2/5)MR2
You have a 5 kg solid metal cylinder with a radius of 2.5
cm. What is its moment of inertia?
0.00313 kg m2
0.00125 kg m2
0.00208 kg m2
0.00156 kg m2
You have a solid metal sphere of mass M, with a radius of
R. What is its moment of inertia?
(2/3)MR2
(2/5)MR2
(1/2)MR2
MR2
You have a...

Find the volume common to two spheres, each with radius r, if
the center of one sphere lies on the boundary of the other.

A sphere of solid aluminum (r = 2.7 g/cm3 ) has a radius R, a
mass M, and a moment of inertia I0 about its center. A second
sphere of solid aluminum has a different mass M’ with a radius 2R.
What is the moment of inertia of the second sphere about its center
I in terms of the first sphere I0? Mass should not appear in your
answer (4 points).

Find the center (h,k) and the radius r of the circle 4 x^2 + 7 x
+4 y^2 - 6 y - 9 = 0 .
h=? k=? r=?

A thin-walled metal spherical shell of radius a = 8 m has a
charge qa = 23 C. Concentric with it is a thin-walled metal
spherical shell of radius b = 7a and charge qb = 27 C. Find the
electric field at points a distance r from the common center, where
(a) r = 2.4 m, (b) r = 16 m, and (c) r = 84.0 m.

A hollow sphere (mass M, radius R) starts from rest at the top
of a hill of height H. It rolls down the hill without slipping.
Find an expression for the speed of the ball's center of mass once
it reaches the bottom of the hill.

One model for a certain planet has a core of radius R
and mass M surrounded by an outer shell of inner radius
R, outer radius 2R, and mass 4M. If
M = 5.95 × 1024 kg and R = 2.57 ×
106 m, what is the gravitational acceleration of a
particle at points (a) R and
(b) 3R from the center of the planet?

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