Question

A merry-go-round with a a radius of R = 1.84 m and moment of
inertia I = 186 kg-m^{2} is spinning with an initial
angular speed of ω = 1.55 rad/s in the counter clockwise direection
when viewed from above. A person with mass m = 51 kg and velocity v
= 5 m/s runs on a path tangent to the merry-go-round. Once at the
merry-go-round the person jumps on and holds on to the rim of the
merry-go-round.

What is the magnitude of the angular momentum of the person 2 meters before she jumps on the merry-go-round?

What is the angular speed of the merry-go-round after the person jumps on?

Once the merry-go-round travels at this new angular speed, with what force does the person need to hold on?

Once the person gets half way around, they decide to simply let go of the merry-go-round to exit the ride.

What is the magnitude of the linear velocity of the person right as they leave the merry-go-round?

What is the angular speed of the merry-go-round after the person lets go?

Answer #1

A merry-go-round with a a radius of R = 1.84 m and moment of
inertia I = 206 kg-m2 is spinning with an initial
angular speed of ? = 1.54 rad/s in the counter clockwise direection
when viewed from above. A person with mass m = 66 kg and velocity v
= 4.5 m/s runs on a path tangent to the merry-go-round. Once at the
merry-go-round the person jumps on and holds on to the rim of the
merry-go-round.
1)...

A merry-go-round with a a radius of R = 1.66 m and moment of
inertia I = 217 kg-m2 is spinning with an initial
angular speed of ω = 1.57 rad/s in the counter clockwise direection
when viewed from above. A person with mass m = 61 kg and velocity v
= 4.8 m/s runs on a path tangent to the merry-go-round. Once at the
merry-go-round the person jumps on and holds on to the rim of the
merry-go-round.
4)...

A merry-go-round with a a radius of R = 1.62 m and moment of
inertia I = 215 kg-m2 is spinning with an initial
angular speed of ω = 1.52 rad/s in the counter clockwise direection
when viewed from above. A person with mass m = 56 kg and velocity v
= 4.6 m/s runs on a path tangent to the merry-go-round. Once at the
merry-go-round the person jumps on and holds on to the rim of the
merry-go-round.
What...

A merry-go-round with a a radius of R = 1.75 m and moment of
inertia I = 182 kg-m2 is spinning with an initial
angular speed of ω = 1.4 rad/s in the counter clockwise direection
when viewed from above. A person with mass m = 71 kg and velocity v
= 4.4 m/s runs on a path tangent to the merry-go-round. Once at the
merry-go-round the person jumps on and holds on to the rim of the
merry-go-round.
1)What...

A merry-go-round with a a radius of R = 1.75 m and moment of
inertia I = 182 kg-m2 is spinning with an initial
angular speed of ω = 1.4 rad/s in the counter clockwise direction
when viewed from above. A person with mass m = 71 kg and velocity v
= 4.4 m/s runs on a path tangent to the merry-go-round. Once at the
merry-go-round the person jumps on and holds on to the rim of the
merry-go-round.
3)...

Merry Go
Round
A merry-go-round
with a radius of R = 1.80 m and moment of inertia I
= 201
kg-m2
spinning with an
initial angular speed of ω = 1.5 rad/s in the counter clockwise
direction when viewed from above. A person with mass m =
55
kg and velocity v
= 4.5
m/s runs on a path
tangent to the merry-go-round. Once at the merry-go-round the
person jumps on and holds on to the rim of the
merry-go-round....

A playground merry-go-round has a radius R and a rotational
inertia I. When the merry-go-round is at rest, a child with mass m
runs with speed v along a line tangent to the rim and jumps on. The
angular velocity of the merry-go-round is then

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 has a moment of inertia of 600 kg
m2. When the merry-go-round is at rest, a 20 kg boy runs
at 5.9 m/s along a line tangential to the rim and jumps on, landing
on the rim a distance of 3.0 m from the rotation axis of the
merry-go-round. The angular velocity of the merry-go-round is
then:
A.1.2 rad/s
B.0.38 rad/s
C.0.45 rad/s
D.0.56 rad/s
E.0.72 rad/s

A disk-shaped merry-go-round of radius 2.93 m and mass 185 kg
rotates freely with an angular speed of 0.621 rev/s . A 60.4 kg
person running tangential to the rim of the merry-go-round at 3.51
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.
What is the final angular speed of the merry-go-round?

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