Question

Two astronauts each having a mass of 75.0 kg, are connected by a 9.5 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 4.50 m/s. (a) Treating the astronauts as particles, calculate the magnitude of the angular momentum. kg·m2/s (b) Calculate the rotational energy of the system. J (c) By pulling on the rope, one of the astronauts shortens the distance between them to 5.00 m. What is the new angular momentum of the system? kg·m2/s (d) What are the astronauts' new speeds? m/s (e) What is the new rotational energy of the system? J (f) How much work does the astronaut do in shortening the rope? kJ

Answer #1

Two astronauts (figure), each having a mass of 74.0 kg, are
connected by a
d = 11.0-m
rope of negligible mass. They are isolated in space, orbiting
their center of mass at speeds of 5.30 m/s.
Two astronauts are connected by a taut horizontal rope of length
d. They rotate counterclockwise about the center of mass
CM at the midpoint of the rope.
(a) Treating the astronauts as particles, calculate the
magnitude of the angular momentum of the two-astronaut
system....

Two astronauts, each with a mass of 57 kg, are connected by a
6.4 m massless rope. Initially they are rotating around their
center of mass with an angular velocity of 1.9 rad/s. One of the
astronauts then pulls on the rope shortening the distance between
the two astronauts to 2.6 m. What is angular speed (in rad/s) of
the system at this new separation distance between the astronauts?
You may model each astronaut as a point particle.

A solid disk of mass m1 = 9.5 kg and radius R = 0.19
m is rotating with a constant angular velocity of ω = 30 rad/s. A
thin rectangular rod with mass m2 = 3.3 kg and length L
= 2R = 0.38 m begins at rest above the disk and is dropped on the
disk where it begins to spin with the disk.
1) What is the initial angular momentum of the rod and disk
system?
2) What...

in
space, two astronauts, each with a mass of 60 kg, are attached to
each other at the ends of a 30 m long rope. they are rotating abiut
the CENTER of the rope, each traveling in the same circular path at
a speed of V =3.50 m/s
draw and label a figure
A) find initial moment of inertia
B) find the initial angular velocity
the astronauts pull themselves along the rope until they are
2.20 m apart.
C) now...

A solid disk of mass m1 = 9.5 kg and radius R = 0.19
m is rotating with a constant angular velocity of ω = 30 rad/s. A
thin rectangular rod with mass m2 = 3.3 kg and length L
= 2R = 0.38 m begins at rest above the disk and is dropped on the
disk where it begins to spin with the disk.
5) What is the final rotational energy of the rod and disk
system?

Two children (m = 27.0 kg each) stand opposite each
other on the edge of a merry-go-round. The merry-go-round, which
has a mass of 1.66 ? 102 kg and a radius of 1.6 m, is
spinning at a constant rate of 0.38 rev/s. Treat the two children
and the merry-go-round as a system.
(a) Calculate the angular momentum of the system, treating each
child as a particle. (Give the magnitude.)
kg · m2/s
(b) Calculate the total kinetic energy of...

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...

In the figure, two particles, each with mass m = 0.86
kg, are fastened to each other, and to a rotation axis at
O, by two thin rods, each with length d = 5.4 cm
and mass M = 1.2 kg. The combination rotates around the
rotation axis with angular speed ω = 0.33 rad/s. Measured
about O, what is the combination's (a)
rotational inertia and (b) kinetic energy?

At time t = 4 sec, a particle of mass M = 4.5 kg is at
the position (x,y,z) = (4,4,6) m and has velocity (2,1,-2) m/s.
1)What is the
x component of the particle's angular momentum about the
origin?
2)What is the y component of the particle's angular
momentum about the origin?
3)What is the
z component of the particle's angular momentum about the
origin?
4)Now an identical
particle is placed at (x,y,z) = (-4,-4,-6) m, with
velocity (-2,-1,2)...

At time t = 11.5 sec, a particle of mass M = 5 kg is at
the position (x,y,z) = (4,4,6) m and has velocity (2,1,-2) m/s.
1) What is the x component of the particle's angular
momentum about the origin?
2) What is the y component of the particle's angular
momentum about the origin?
3) What is the z component of the particle's angular
momentum about the origin?
4) Now an identical particle is placed at (x,y,z) =
(-4,-4,-6)...

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