Question

A space station in the shape of a uniform disk (mass
6.42x10^{5} kg, radius 150 m) rotates with period 33.6
seconds. There are also 809 astronauts (whom you can treat as point
particles) working inside the space station, each of mass 199 kg,
and all standing on the outside rim and rotating with the station.
Now, all the astronauts move to a conference room at the very
center of the space station. Find the new period of the rotation of
the space station.

Answer #1

A uniform disk of mass Mdisk = 4 kg and radius R =
0.24 mhas a small block of mass mblock = 2.2 kg on its
rim. It rotates about an axis a distance d = 0.16 m from its center
intersecting the disk along the radius on which the block is
situated.
What is the moment of inertia of the block about the rotation
axis?
What is the moment of inertia of the disk about the rotation
axis?
When...

1. A space station is essentially a uniform disk in orbit about
a planet; its mass when empty is M = 1.68x108
kg and its radius is 6.28 km. You want to create an artificial
gravity so a worker on the outer edge of the disk feels an
acceleration of 3 m/s2. Find the period of the station's
rotation, in minutes; this is the time it takes for one complete
revolution. Assume the worker's mass is negligible.

Consider a non-rotating space station in the shape of a long
thin uniform rod of mass 6.65 x 10^6 kg and length 574 meters.
Rocket motors on both ends of the rod are ignited, applying a
constant force of F = 9.48 x 10^5 N to each end of the rod as shown
in the diagram, causing the station to rotate about its center. If
the motors are left running for 2 minutes and 21 seconds before
shutting off, then...

A.) Consider a non-rotating space station in the shape of a long
thin uniform rod of mass 4.20 x 10^6 kg and length 953 meters.
Rocket motors on both ends of the rod are ignited, applying a
constant force of F = 4.40 x 10^5 N to each end of the rod as shown
in the diagram, causing the station to rotate about its center. If
the motors are left running for 1 minutes and 26 seconds before
shutting off,...

A.) Consider a non-rotating space station in the shape of a long
thin uniform rod of mass 4.96 x 10^6 kg and length 530 meters.
Rocket motors on both ends of the rod are ignited, applying a
constant force of F = 4.99 x 10^5 N to each end of the rod as shown
in the diagram, causing the station to rotate about its center. If
the motors are left running for 1 minutes and 28 seconds before
shutting off,...

A uniform disk of mass M and radius R is initially rotating
freely about its central axis with an angular speed of ω, and a
piece of clay of mass m is thrown toward the rim of the disk with a
velocity v, tangent to the rim of the disk as shown. The clay
sticks to the rim of the disk, and the disk stops rotating.
33. What is the magnitude of the total angular momentum of the
clay-disk system...

A uniform disk with radius 0.440 m and mass 32.0 kg rotates in a
horizontal plane on a frictionless vertical axle that passes
through the center of the disk. The angle through which the disk
has turned varies with time according to θ(t)=( 1.00 rad/s
)t+( 8.10 rad/s2 )t2 .
What is the resultant linear acceleration of a point on the rim
of the disk at the instant when the disk has turned through 0.300
rev ?
Express your answer...

A uniform disk with radius 0.320 m and mass 32.0 kg rotates in a
horizontal plane on a frictionless vertical axle that passes
through the center of the disk. The angle through which the disk
has turned varies with time according to
?(t)=( 1.00 rad/s)t+( 6.10
rad/s2 )t2 .
a)What is the resultant linear acceleration of a point on the
rim of the disk at the instant when the disk has turned through
0.300 rev ?
Express your answer with...

A flat uniform circular disk (radius = 3.00 m, mass = 1.00 ✕ 102
kg) is initially stationary. The disk is free to rotate in the
horizontal plane about a frictionless axis perpendicular to the
center of the disk. A 50.0 kg person, standing 1.75 m from the
axis, begins to run on the disk in a circular path and has a
tangential speed of 2.60 m/s relative to the ground. Find the
resulting angular speed of the disk (in...

This time we have a non-rotating space station in the shape of a
long thin uniform rod of mass 1.88 x 10^6 kg and length 1447
meters. Small probes of mass 9779 kg are periodically launched in
pairs from two points on the rod-shaped part of the station as
shown, launching at a speed of 3576 m/s with respect to the launch
points, which are each located 412 m from the center of the rod.
After 17 pairs of probes...

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