Question

A student on a piano stool rotates freely with an angular speed of 2.92 rev/s. The student holds a 1.50-kg mass in each outstretched arm, 0.752 m from the axis of rotation. The combined moment of inertia of the student and the stool, ignoring the two masses, is 5.48 kg*m^2, a value that remains constant. As the student pulls his arms inward, his angular speed increases to 3.41 rev/s.

A) How far are the masses from the axis of rotation at this time, considering the masses to be points? (in m)

B) Calculate the initial kinetic energy of the system. (in J)

C) Calculate the final kinetic energy of the system. (in J)

Answer #1

A student sits on a freely rotating stool holding two dumbbells,
each of mass 2.98 kg. When his arms are extended horizontally, the
dumbbells are 0.94 m from the axis of rotation and the student
rotates with an angular speed of 0.752 rad/s. The moment of inertia
of the student plus stool is 2.79 kg · m2 and is assumed to be
constant. The student pulls the dumbbells inward horizontally to a
position 0.308 m from the rotation axis.
(a)...

A student sits on a freely rotating stool holding two weights,
each of mass 2.93 kg. When his arms are extended horizontally, the
weights are 1.10 m from the axis of rotation and he rotates with an
angular speed of 0.754 rad/s. The moment of inertia of the student
plus stool is 2.93 kg·m2 and is assumed to be constant.
The student pulls the weights inward horizontally to a position
0.296 m from the rotation axis.
(a) Find the new...

A student sits on a freely rotating stool holding two dumbbells,
each of mass 2.91 kg (see figure below). When his arms are extended
horizontally (Figure a), the dumbbells are 1.03 m from the axis of
rotation and the student rotates with an angular speed of 0.758
rad/s. The moment of inertia of the student plus stool is 2.61 kg ·
m2 and is assumed to be constant. The student pulls the
dumbbells inward horizontally to a position 0.297 m...

A student sits on a rotating chair holding two 6.0kg masses.
When his arms are extended horizontally, the masses are 1.0 m from
the axis of rotation, and he rotates with an angular speed of 0.75
rad/s. The moment of inertia of the students plus stool is 6.0 kg
m2 and is assumed to be constant. The student pulls the
masses horizontally to a 0.30m from the axis of rotation.
(a) Find the new angular speed of the student.
(b)...

A student sits on a rotating stool holding two 2.7-kg objects.
When his arms are extended horizontally, the objects are 1.0 m from
the axis of rotation and he rotates with an angular speed of 0.75
rad/s. The moment of inertia of the student plus stool is
3.0 kg · m2
and is assumed to be constant. The student then pulls in the
objects horizontally to 0.43 m from the rotation axis.
(a) Find the new angular speed of the...

A student sits on a rotating stool holding two 2.8-kg objects.
When his arms are extended horizontally, the objects are 1.0 m from
the axis of rotation and he rotates with an angular speed of 0.75
rad/s. The moment of inertia of the student plus stool is
3.0 kg · m2
and is assumed to be constant. The student then pulls in the
objects horizontally to 0.50 m from the rotation axis.
(a) Find the new angular speed of the...

A student sits on a rotating stool holding two 4.0 kg objects.
When his arms are extended horizontally, the objects are 1.0 m from
the axis of rotation, and he rotates with an angular speed of 0.75
rad/s. The moment of inertia of the student plus stool is 3.0
kg·m2 and is assumed to be constant. The student then
pulls the objects horizontally to 0.20 m from the rotation
axis.
(a) Find the new angular speed of the student.
rad/s...

A student sits on a rotating stool holding two 6.0 kg k g
objects. When his arms are extended horizontally, the objects are
1.3 m m from the axis of rotation and he rotates with an angular
speed of 2.7 rad/s r a d / s . The moment of inertia of the student
plus stool is 3.3 kg⋅m2 k g ⋅ m 2 and is assumed to be constant.If
the student pulls in the two objects horizontally to...

A student sitting on a chair on a circular platform of
negligible mass rotates freely on an air table at initial
rotational speed 2.3 rad/s. The student's arms are initially
extended with 6.0-kg dumbbells in each hand. As the student pulls
her arms in toward her body, the dumbbells move from a distance of
0.80 m to 0.10 m from the axis of rotation. The initial rotational
inertia of the student's body (not including the dumbbells) with
arms extended is...

A student sits in a chair that can spin without friction. The
student has her hands outstretched and starts rotating at 1.7
rev/s. Her initial rotational inertia about the central axis is
13.00 kg m2. She pulls her hands inward and decreases her
rotational inertial to 7.60 kg m2. What is her resulting angular
speed after she pulls her hands inward?(rad/s) (in rad/s)
What is the ratio of the new kinetic energy of the system to the
original kinetic energy? ...

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