Question
In: Physics
The moment of inertia of a thin ring of mass M and radius R about its...
The moment of inertia of a thin ring of mass M and radius R about its symmetry axis is ICM = MR2
Kira is working the ring-toss booth at a local carnival. While waiting for customers, Kira occupies her time by twirling one of the plastic rings of mass M and radius R about her finger. Model the motion of the plastic ring as a thin ring rotating about a point on its circumference. What is the moment of inertia of the plastic ring?
Solutions
genius_generous answered 1 year agoRelated Solutions
Show that the moment of inertia of a spherical shell of radius R and mass M...
Show that the moment of inertia of a spherical shell of radius R
and mass M about an axis through
its centre is 2/3 MR2. Show also that the moment of inertia of a
uniform solid sphere of radius R and
mass M is 2/5MR2. The spheres are allowed to roll (from rest),
without slipping a distance L down
a plane inclined at a angle θ to the horizontal. Find expressions
for the speeds of the spheres at the
bottom...
Find the moment of inertia of a circular disk of radius R and mass M that...
Find the moment of inertia of a circular disk of radius R and
mass M that rotates on an axis passing through its center. [Answer:
½ MR2]
Step 1: Pictorial representation: Sketch a neat picture to
represent the situation.
Step 2: Physical representation: 1) Cut the disk into many small
rings as it has the circular symmetry. 2) Set up your coordinate
system and choose its origin at the pivot point (or the axle
location) for convenience. Then choose a...
A hollow ball has mass M=2.0kg, radius R=0.35m, and moment of inertia about the center of...
A hollow ball has mass M=2.0kg, radius R=0.35m, and moment of
inertia about the center of mass I=(2/3)MR2. The ball is
thrown without bouncing, to the right with an initial speed 2.0m/s
and backspin. The hoop moves across the rough floor (coefficient of
sliding friction = 0.25) and returns to its original position with
a speed of 0.5 m/s. All surfaces and the hoop may be treated as
ideally rigid. Develop an expression for angular velocity of the
hoop as...
A thin uniform disk of radius r and mass m is spinning about its center at...
A thin uniform disk of radius r and mass m is spinning about its
center at angular speed ω0. The disk is placed flat on a horizontal
surface. The coefficient of kinetic friction between the disk and
the surface is μ and constant for the entire area of contact. a)
Find the frictional torque on the disk. (Hint: Divide the disk into
many concentric rings.) b) How long will it take the disk to come
to rest?
A space station is approximately a ring of radius,R, and mass m, which rotates about its...
A space station is approximately a ring of radius,R, and mass m,
which rotates about its symmetry axis with angular
velocity,~ω=ω0ˆe3. A meteor is traveling with momentum,~p, that is
parallel to the original ˆe3, and strikes the space station at a
point on the rim,transferring the entire momentum to the space
station (an inelastic collision where the meteor sticks to the
space station). Further, though the meteor has significant
momentum,it is of very small mass so that the moment of...
A merry-go-round with a a radius of R = 1.98 m and moment of inertia I...
A merry-go-round with a a radius of R = 1.98 m and moment of
inertia I = 193 kg-m2 is spinning with an initial
angular speed of ω = 1.45 rad/s in the counter clockwise direection
when viewed from above. A person with mass m = 67 kg and velocity v
= 4.9 m/s runs on a path tangent to the merry-go-round. Once at the
merry-go-round the person jumps on and holds on to the rim of the
merry-go-round.
1)...
Consider a thin uniform disk of mass M and radius R. A mass m is located...
Consider a thin uniform disk of mass M and radius R. A mass m is
located along the axis of the disk at a distance z from the center
of the disk. The gravitational force on the mass m (in terms of m,
M, R, G, and z) is
A sphere of mass M, radius r, and moment of inertial I = Mr2 (where is...
A sphere of mass M, radius r, and moment of inertial I = Mr2
(where is a dimensionless constant which depends on how the mass is
distributed in the sphere) is placed on a track at a height h above
the lowest point on the track. The sphere is released, and rolls
without slipping. It reaches a horizontal surface which
subsequently bends into a vertical loop-the-loop of radius R, as in
Fig. 2 below.
a) When it reaches the top...
Find the mass, the center of mass, and the moment of inertia about the z-axis for...
Find the mass, the center of mass, and the moment of inertia
about the z-axis for the hemisphere x^2+y^2+z^2=1, z >(greater
than or equal to) 0 if density is sqrt(x^2+y^2+z^2)
A ring (mass 2 M, radius 1 R) rotates in a CCW direction with an initial...
A ring (mass 2 M, radius 1 R) rotates in a CCW direction with an
initial angular speed 2 ω. A disk (mass 4 M, radius 2 R) rotates in
a CW direction with initial angular speed 4 ω. The ring and disk
"collide" and eventually rotate together. Assume that positive
angular momentum and angular velocity values correspond to rotation
in the CCW direction.
What is the initial angular momentum Li of the ring+disk system?
Write your answer in terms...
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