Question

*Nonuniform cylindrical object*. In the figure, a
cylindrical object of mass *M* and radius *R* rolls
smoothly from rest down a ramp and onto a horizontal section. From
there it rolls off the ramp and onto the floor, landing a
horizontal distance *d* = 0.482 m from the end of the ramp.
The initial height of the object is *H* = 0.88 m; the end of
the ramp is at height *h* = 0.10 m. The object consists of
an outer cylindrical shell (of a certain uniform density) that is
glued to a central cylinder (of a different uniform density). The
rotational inertia of the object can be expressed in the general
form *I* = *βMR*^{2}, but *β* is not
0.5 as it is for a cylinder of uniform density. Determine
*β*.

Answer #1

A ball of mass M and radius R rolls smoothly from rest down a
ramp and onto a circular loop of radius 0.47 m. The initial height
of the ball is h = 0.35 m. At the loop bottom, the magnitude of the
normal force on the ball is 2.0 Mg. The ball consists of an outer
spherical shell (of a certain uniform density) that is glued to a
central sphere (of a different uniform density). The rotational
inertia of...

A nonuniform cylinder (radius = 0.14 m, center-of-mass
rotational inertia = 2.22×10-2 kg·m2, mass = 1.33 kg) starts from
rest and rolls without slipping down a plane with an angle of
inclination of 24.2°. How long does it take to travel 1.56 m along
the incline?

3) A Solid Ball, of mass M and radius
R rolls from rest down a table-top ramp of height
H and then rolls (horizontally) across a table until it
gets to the edge and rolls off the edge and drops a distance
h to the floor.
(a) At what horizontal distance D (from the table edge)
does the ball hit the floor?
(b) Rank the following objects from least D to greatest
D :
Solid Ball, Hollow Sphere, Solid Cylinder,...

A Brunswick bowling ball with mass M= 7kg and radius R=0.15m
rolls from rest down a ramp without slipping. The initial height of
the incline is H= 2m. The moment of inertia of the ball is
I=(2/5)MR2
What is the total kinetic energy of the bowling ball at the
bottom of the incline?
684J
342J
235J
137J
If the speed of the bowling ball at the bottom of the incline is
V=5m/s, what is the rotational speed ω at the...

1. A cylindrical wooden log rolls without slipping down a small
ramp. The log has a radius of 16 cm, a length of 2.5 m, and a mass
of 130 kg. The log starts from rest near the top of the ramp. When
the log reaches the bottom of the ramp, it is rolling at a linear
speed of 2.3 m/s.
a.) Assuming that the log is a perfect cylinder of uniform
density, find the log’s moment of inertia (about...

A uniform cylinder of mass M and radius R rolls without slipping
down a slope of angle theeta to the horizontal. The cylinder is
connected to a spring constant K while the other end of the spring
is connected to a rigid support at P. The cylinder is released when
the spring is unstrectched. The maximum displacement of cylinder is
?

A uniform spherical shell of mass M = 17.0 kg and radius R =
0.310 m can rotate about a vertical axis on frictionless bearings
(see the figure). A massless cord passes around the equator of the
shell, over a pulley of rotational inertia I = 0.210 kg·m2 and
radius r = 0.100 m, and is attached to a small object of mass m =
1.50 kg. There is no friction on the pulley's axle; the cord does
not slip...

Consider the objects below, all of mass M and radius R (where
appropriate). They are placed on an incline plane at the same
height. Which object will roll down the incline and reach the
bottom with the greatest total energy?
a) A solid sphere
b) A thin spherical shell
c) A solid cylinder of length L
d) A cylindrical shell of length L
e) All will reach bottom with same energy
Group of answer choices
A solid sphere
A thin...

Problem 4
A hoop and a solid disk both with Mass (M=0.5 kg) and radius (R=
0.5 m) are placed at the top of an incline at height (h= 10.0 m).
The objects are released from rest and rolls down without
slipping.
a) The solid disk reaches to the bottom of the inclined plane
before the hoop. explain why?
b) Calculate the rotational inertia (moment of inertia) for the
hoop.
c) Calculate the rotational inertia (moment of inertia) for the...

A sphere of mass M, radius r, and rotational inertia I is
released from rest at the top of an inclined plane of height h as
shown above. (diagram not shown)
If the plane has friction so that the sphere rolls without
slipping, what is the speed vcm of the center of mass at the bottom
of the incline?

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