Question

A disc-shaped merry-go-round has a mass of 100 kg and a radius of 1.60 m and is initially spinning at 20.0 rpm, with a 33-kg child sitting at its center. The child then walks out to the edge of the disc. (a) Find the initial and final moments of inertia of the system (disc + child), treating the child as a point particle. (b) State why the system’s angular momentum is conserved. (You can assume that the axis of the disc is frictionless.) (c) Find the initial and final kinetic energies of the system. (d) State the physical reason for the change in kinetic energy. (I.e., what force does the work that causes the kinetic energy to change?)

Answer #1

A disk-shaped merry-go-round of radius 2.63 m and mass 155 kg
rotates freely with an angular speed of 0.558 rev/s. A 59.4 kg
person running tangential to the rim of the merry-go-round at 3.58
m/s jumps onto its rim and holds on. Before jumping on the
merry-go-round, the person was moving in the same direction as the
merry-go-round's rim. (a) Does the kinetic energy of the system
increase, decrease, or stay the same when the person jumps on the
merry-go-round?...

A child of mass 60 kg sits at the center of a playground
merry-go-round which is spinning at 1.5 rad/s. The moment of
inertia and radius of the merry-go-round are 150 kg×m2 and 1.2 m
respectively. How much rotational kinetic energy does the system
lose as the child moves to the edge of the merry-go-round? (Treat
the child as a point mass.)

IP A disk-shaped merry-go-round of radius 2.84 m and mass 155 kg
rotates freely with an angular speed of 0.62 rev/s . A 61.1 kg
person running tangential to the rim of the merry-go-round at 3.17
m/s jumps onto its rim and holds on. Before jumping on the
merry-go-round, the person was moving in the same direction as the
merry-go-round's rim.
Part B Calculate the initial kinetic energy for this system.
Part C Calculate the final kinetic energy for this...

A playground merry-go-round of radius ? = 2.0 m has a moment of
inertia ? = 250 kg ⋅ m^2 is rotating at 15 rpm about a
frictionless, vertical axle. Facing the axle, a 25-kg child hops
onto the merry-goround and manages to sit down on the edge. (a) (10
pts) What is the total angular momentum of the
‘merry-go-round-child’ system before and after the child hops on
the the merry-go-round? (b) (10 pts) What is the new angular speed,...

Billy (mass = 50 kg) stands on the edge of a merry-go-round,
which is a disc with a radius R = 2.0 m and a mass M = 100 kg.
Annie begins spinning the merry-go-round (and Billy) by pushing on
it with a force of 20 N tangent to its edge for 20 s.
(a) What are (i) the torque Annie imparts on the merry-go-round
(with Billy on it) and (ii) the resulting angular acceleration
during the 20 second interval?...

Three children are riding on the edge of a merry-go-round that
is 142 kg, has a 1.60 m radius, and is spinning at 17.3 rpm. The
children have masses of 22.4, 29.0, and 38.8 kg. If the child who
has a mass of 38.8 kg moves to the center of the merry-go-round,
what is the new angular velocity in rpm?

Three children are riding on the edge of a merry-go-round that
is 142 kg, has a 1.60 m radius, and is spinning at 19.3 rpm. The
children have masses of 22.4, 30.5, and 34.8 kg. If the child who
has a mass of 34.8 kg moves to the center of the merry-go-round,
what is the new angular velocity in rpm?

a 50.0 kg child is on a 200. kg merry-go-round with a radius of
1.50 m. the child starts at 0.5 m from the center and moves to the
edge. the child's parent accelerates the merry-go-round from rest
at 0.75 rad/s^2 to a speed of 1.5 rad/s. How long did the parent
push the merry-go-round? how much force is required to hold the
child when at 0.5 m from the center? determine the kinetic energy
of the system when moving...

Three children are riding on the edge of a merry-go-round that
is 105 kg, has a 1.60-m radius, and is spinning at 22.0 rpm. The
children have masses of 22.0, 28.0, and 33.0 kg. If the child who
has a mass of 28.0 kg moves to the center of the merry-go-round,
what is the new angular velocity in rpm? Ignore friction, and
assume that the merry-go-round can be treated as a solid disk and
the children as points.

A 40 kg child (point mass) rides on the outer edge of a
merry-go-round, which is a large disk of mass 150 kg and radius 1.5
m. The merry-go-round spins with an angular velocity of 12 rpm.
What is the merry-go-round’s angular velocity in radians per second
(rad/s)? What is the total rotational inertia (moment of inertia)
of the child and merry-go-round together? What is the rotational
kinetic energy (in joules) of the merry-go-round and child
together? What magnitude of...

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