Question

A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round, which can be modeled as a disk with a mass of 300 kg , is spinning at 24 rpm. John runs tangent to the merry-go-round at 4.6 m/s, in the same direction that it is turning, and jumps onto the outer edge. John's mass is 30 kg.

Answer #1

The moment of inertia of the merry-go-round is

I = (1/2) M R^{2} = (1/2)*300 * (1.5)^{2} = 337.5
kgm^{2}

The initial angular velocity of the merry-go-round is

1 = 24*2*/60
= **2.513 rad/s**

The angular momentum conservation equation is:

I*1
+ m*R*v = (I + mR^2)*2

where m is John's mass.

337.5* 2.513 + 30* (1.5) * 4.6 = ( 337.5 + 30*(1.5)^{2} )
2

848.23 + 207 = (405)*2

2 = **2.605** rad/s = 24.87 rpm

So the Merry-Go-Round speeds up.

A 2.8-m -diameter merry-go-round with a mass of 230 kg is
spinning at 20 rpm . John runs around the merry-go-round at 5.0 m/s
, in the same direction that it is turning, and jumps onto the
outer edge. John’s mass is 35 kg . What is the merry-go-round's
angular speed, in rpm, after John jumps on?

A 2-m-diameter merry-go-round with a mass of 250 kg is spinning
at 20 rpm. John runs around the merry-go-round at5.0 m/s, in the
same direction that it is turning, and jumps onto the outer edge.
John’s mass is 31 kg .
Part A
What is the merry-go-round's angular speed, in rpm, after John
jumps on?

)A 3.5-m diameter merry-go-round with a mass of 275 kg is
spinning at 22 rpm. John runs around the merry-go-round at 5.0 m/s
in the opposite direction that the merry-go-round is turning, and
jumps onto the outer edge. John’s mass is 30 kgAfter John jumps on,
a torque is applied that eventually slows down the merry-go-round.
If the merry-go-round comes to a stop 15.6 seconds after the torque
is applied, what is the magnitude of the torque?

A 2.8-mm-diameter merry-go-round with a mass of 240 kgkg is
spinning at 20 rpmrpm. John runs around the merry-go-round at 5.0
m/sm/s, in the same direction that it is turning, and jumps onto
the outer edge. John’s mass is 32 kg.
What is the merry-go-round's angular speed, in rpmrpm, after
John jumps on?
Express your answer in revolutions per minute. (rpm)

A playground merry-go-round has a disk-shaped platform that
rotates with negligible friction about a vertical axis. The disk
has a mass of 200 kg and a radius of 2.1 m. A 36- kg child rides at
the center of the merry-go-round while a playmate sets it turning
at 0.50rpm. If the child then walks along a radius to the outer
edge of the disk, how fast will the disk be turning? (in rpm - but
enter no unit)

A playground merry-go-round has a radius of 3.0 m and a
rotational inertia of 600 kg-m^2. When the merry-go-round is at
rest, a 20-kg child runs at 5.0 m/s along a line tangent to the rim
and jumps on. The angular velocity of the merry-go-round is
then:
.45 rad/s
1.2 rad/s
.38 rad/s
.56 rad/s
.71 rad/s

A playground merry-go-round (of mass 123 kg and radius 1.90 m)
is rotating with an angular velocity of 4.42 rad/s. A 23.7 kg
child, initially at rest, suddenly jumps on the merry-go-round by
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On a playground, a merry-go-round with a total mass of 100 kg
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A playground merry-go-round has a radius R and a rotational
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platform rotates. What is the rotational speed of the
merry-go-round and the child if the merry-go-round started from
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