Question

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 have launched, how fast will the station be spinning?

Answer #1

Question 7
This time we have a non-rotating space station in the shape of a
long thin uniform rod of mass 3.73 x 10^6 kg and length 1428
meters. Small probes of mass 7553 kg are periodically launched in
pairs from two points on the rod-shaped part of the station as
shown, launching at a speed of 4962 m/s with respect to the launch
points, which are each located 384 m from the center of the rod.
After 13 pairs...

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,...

THIS IS ALL ONE QUESTION, PLEASE ANSWER ALL PARTS!
a)We have a crate of mass 29.6 kg on an inclined surface, with a
coefficient of kinetic friction 0.144. Instead of pushing on the
crate, you let it slide down due to gravity. What must the angle of
the incline be, in order for the crate to slide with an
acceleration of 6.62 m/s^2?
b)Consider a non-rotating space station in the shape of a long
thin uniform rod of mass 8.10...

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 space station in the shape of a uniform disk (mass
6.42x105 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...

A thin uniform rod has a length of 0.430 m and is rotating in a
circle on a frictionless table. The axis of rotation is
perpendicular to the length of the rod at one end and is
stationary. The rod has an angular velocity of 0.32 rad/s and a
moment of inertia about the axis of 3.20×10−3 kg⋅m2 . A bug
initially standing on the rod at the axis of rotation decides to
crawl out to the other end of...

Now we have a rod-shaped space station of length 1407 m and mass
4.47 x 10^6 kg, which can change its length (kind of like an
old-fashioned telescope), without changing its overall mass.
Suppose that the station is initially rotating at a constant rate
of 2.35 rpm. If the length of the rod is reduced to 2.35 m, what
will be the new rotation rate of the space station?
3.86 rpm
8.37 rpm
2.32 rpm
6.44 rpm

A thin uniform rod has a length of 0.490 m and is rotating in a
circle on a frictionless table. The axis of rotation is
perpendicular to the length of the rod at one end and is
stationary. The rod has an angular velocity of 0.37 rad/s and a
moment of inertia about the axis of 3.50×10−3 kg⋅m2 . A
bug initially standing on the rod at the axis of rotation decides
to crawl out to the other end of...

We have a rod-shaped space station of length 1419 m and mass
8.35 x 10^6 kg, which can change its length (kind of like an
old-fashioned telescope), without changing its overall mass.
Suppose that the station is initially rotating at a constant rate
of 1.82 rpm. If the length of the rod is reduced to 1.82 m, what
will be the new rotation rate of the space station?
A. 8.7 rpm
B. 2.32 rpm
C. 7.25 rpm
D. 2.9 rpm

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