Question

A 4.2 m diameter merry-go-round is rotating freely with an angular velocity of 0.60 rad/s . Its total moment of inertia is 1700 kg⋅m2 . Four people standing on the ground, each of mass 66 kg , suddenly step onto the edge of the merry-go-round.

1. What is the angular velocity of the merry-go-round now?

2. What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?

Answer #1

A 5.0-m radius playground merry-go-round with a moment of
inertia of 2000 kg?m2 is rotating freely with an angular speed of
3.0 rad/s. Two people, each having a mass of 60 kg are standing
right outside the edge of the merry-go-round. One person radially
steps on the edge merry-go-round with negligible speed and the
angular speed changes to ?1. A few seconds later, the second person
radially steps on the merry-go-round with negligible speed but at
distance of 4.0 m...

A 5.0-m radius playground merry-go-round with a moment of
inertia of 2000 kg?m2 is rotating freely with an angular speed of
3.0 rad/s. Two people, each having a mass of 60 kg are standing
right outside the edge of the merry-go-round. One person radially
steps on the edge merry-go-round with negligible speed and the
angular speed changes to ?1. A few seconds later, the second person
radially steps on the merry-go-round with negligible speed but at
distance of 4.0 m...

A 2.8-m-diameter merry-go-round with rotational inertia 110
kg?m2 is spinning freely at 0.60 rev/s . Four 25-kg children sit
suddenly on the edge of the merry-go-round.
a.) Find the new angular speed.
b.) Determine the total energy lost to friction between the
children and the merry-go-round.

2) A merry-go-round is rotating with a constant angular velocity
of ω = 1.5 rad/s. There is a red line painted across the diameter
of the merry-go-round. A beetle is traveling towards the center of
the merrygo-round along the red line with a constant speed of 2 m/s
relative to the merry-go-round.
a) Find the velocity of the beetle as measured by someone
standing on the ground when the beetle is 0.5 m away from the
center of the merry-go-round....

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
grabbing onto its outer edge. How much kinetic energy (in J) is
lost in this inelastic collision?

A playground merry-go-round with a moment of inertia of 300 kg
m2 is rotating with no friction at an angular velocity
of 2.3 rad/s. Sharon, whose mass is 70 kg, runs and jumps on the
merry-go-round in such a way that after she jumps on it the
merry-go round stops. How fast, in m/s was she running if the
merry-go-round had a radius of 2.5 m? Enter only the numerical
value of your answer to 2 significant figures. Do not...

A merry-go-round with a moment of inertia equal to 1250kg?m2 and
a radius of 2.5 m rotates with negligible friction at 1.70 rad/s. A
child initially standing still next to the merry-go-round jumps
onto the edge of the platform straight toward the axis of rotation,
causing the platform to slow to 1.35 rad/s.What is her mass?

1. A person of mass 75.0 kg stands at the center of a rotating
merry-go-round platform of radius 3.00 m and moment of inertia 826
kg⋅m2. The platform rotates without friction with angular velocity
of 0.955 rad/s. The person walks radially to the edge of the
platform. You may ignore the size of the person.
(a) Calculate the angular velocity when the person reaches the
edge of the merry-go-round.
(b) Calculate the rotational kinetic energy of the system of
platform...

A person of mass 72 kg stands at the center of a rotating
merry-go-round platform of radius 2.7 m and moment of inertia 860
kg?m2 . The platform rotates without friction with angular velocity
0.95 rad/s . The person walks radially to the edge of the
platform.
Calculate the angular velocity when the person reaches the
edge.
Calculate the rotational kinetic energy of the system of
platform plus person before and after the person's walk

A person of mass 70 kg stands at the center of a rotating
merry-go-round platform of radius 3.2 m and moment of inertia 860
kg⋅m2 . The platform rotates without friction with angular velocity
0.95 rad/s . The person walks radially to the edge of the platform.
A. Calculate the angular velocity when the person reaches the edge.
B. Calculate the rotational kinetic energy of the system of
platform plus person before and after the person's walk.

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