Question

Calculate the kinetic energy of a hollow cylinder rotating around its axis of symmetry with constant mass density (height H, inner radius R1, outer radius R2, mass M, angular velocity w). Use cylindrical coordinates

Answer #1

2.
A very long cylindrical cable is composed of an inner solid
cylinder of radius R1 and an outer hollow cylinder of radius R2. An
electrical current runs through the inner wire and returns through
the outer wire.(a) Write down the magnetic energy density function
for both inner and outer regions of the cable.(b) What is the
energy per unit length L, for all regions (for inner and outer
regions)

an amusement park contains a big cylinder of radius R oriented
horizontally and rotating with angular velocity w about its axis.
Achild of mass m is sitting partway up one side so that she remains
at rest a distance h above the bottom of the rotating cylinder.
There is the coefficient of kinetic friction between child and the
cylinder. In terms of R and h ,
how much is the angle?
What is the normal force N acting on the...

A solid cylinder of mass 1.6 kg and radius 35 cm is rotating
counterclockwise around a vertical axis running through the centers
of its circular faces at 560 rev/min. A second solid cylinder of
the same mass and radius is rotating clockwise around the same
vertical axis running through the centers of its circular faces at
850 rev/min. If the cylinders couple so that they rotate about the
same vertical axis, what is the angular velocity (in rev/min) of
the...

A cylinder rotating about its axis with a constant angular
acceleration of 1.6 rad/s^2 starts from rest at t=0. At the instant
when it has turned through 0.40 radian, find the magnitude of the
tangential velocity at point on the rim (radius=0.15 m)?

The figure shows an overhead view of a ring that can rotate
about its center like a merry-go-round. Its outer radius
R2 is 1.0 m, its inner radius
R1 is R2/2, its mass
M is 7.9 kg, and the mass of the crossbars at its center
is negligible. It initially rotates at an angular speed of 7.3
rad/s with a cat of mass m = M/4 on its outer edge, at
radius R2. By how much does the cat increase...

The figure shows an overhead view of a ring that can rotate
about its center like a merry-go-round. Its outer radius R2 is 0.9
m, its inner radius R1 is R2/2, its mass M is 8.0 kg, and the mass
of the crossbars at its center is negligible. It initially rotates
at an angular speed of 8.5 rad/s with a cat of mass m = M/4 on its
outer edge, at radius R2. By how much does the cat increase...

1The figure below shows an overhead view of a
ring that can rotate about its center like a merry-go-round. Its
outer radius R2 is 0.770 m, its inner radius
R1 is R2/2.00, its mass
M is 8.70 kg, and the mass of the crossbars at its center
is negligible. It initially rotates at an angular speed of 7.80
rad/s with a cat of mass m = M/4.00 on its outer
edge, at radius R2. By how much does the cat...

An infinitely long solid insulating cylinder of radius a = 4.3
cm is positioned with its symmetry axis along the z-axis as shown.
The cylinder is uniformly charged with a charge density ρ = 29
μC/m3. Concentric with the cylinder is a cylindrical
conducting shell of inner radius b = 10.1 cm, and outer radius c =
12.1 cm. The conducting shell has a linear charge density λ =
-0.34μC/m.
What is V(P) – V(R), the potential difference between points...

A long, conductive cylinder of radius R1 = 3.40 cm and uniform
charge per unit length λ = 453 pC/m is coaxial with a long,
cylindrical, non-conducting shell of inner and outer radii R2 =
11.9 cm and R3 = 13.6 cm, respectively. If the cylindrical shell
carries a uniform charge density of ρ = 40.5 pC/m3, find the
magnitude of the electric field at the following radial distances
from the central axis:
R1 = 2.58 cm
R2 = 7.65...

A hanging weight, with a mass of m1 = 0.355
kg, is attached by a rope to a block with mass
m2 = 0.845 kg as shown in the figure below. The
rope goes over a pulley with a mass of M = 0.350 kg. The
pulley can be modeled as a hollow cylinder with an inner radius of
R1 = 0.0200 m, and an outer radius of
R2 = 0.0300 m; the mass of the spokes is
negligible. As...

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