Question

A student sitting on a chair on a circular platform of negligible mass rotates freely on an air table at initial rotational speed 1.7 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 6.0 kg⋅m2 and her final rotational inertia is 5.0 kg⋅m2 .

A) Determine the student's final rotational speed.

B) Determine the change of kinetic energy of the system consisting of the student together with the two dumbbells.

C) Determine the change in the kinetic energy of the system consisting of the two dumbbells alone without the student.

D) Determine the change of kinetic energy of the system consisting of student alone without the dumbbells.

Answer #1

**(a) Conservation of angular momentum**

**I1 w1 = I2 w2 =**

**( 6 + 2 * 6 *0.8^2) * 2 = ( 5 + 2 * 6 * 0.1^2 )
w2**

**w2 = ( 6 + 2 * 6 *0.8^2) * 2 /( 5 + 2 * 6 * 0.1^2 ) =
5.343 rad/s**

**(b) change of kinetic energy = KE2 - KE1 =
0.5 I2 w2^2 - 0.5 I1 w1^2**

**= 0.5 * ( 5 + 2 * 6 * 0.1^2 ) * 5.343^2 - 0.5*( 6 + 2 *
6 *0.8^2) * 2^2 = 45.72 J**

**(c) change of kinetic energy = 0.5 * ( 2 * 6 * 0.1^2 ) *
5.343^2 - 0.5*( 2 * 6 *0.8^2) * 2^2 = -13.65 J**

**(d) change of kinetic energy = 0.5 * ( 5 ) *
5.343^2 - 0.5*( 6 ) * 2^2 = 59.36 J**

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 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 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 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? ...

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...

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 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...

In this example we see how a system can have constant angular
momentum without having a constant angular velocity! A physics
professor stands at the center of a turntable, holding his arms
extended horizontally, with a 5.0 kg dumbbell in each hand (Figure
1). He is set rotating about a vertical axis, making one revolution
in 2.0 s. His moment of inertia (without the dumbbells) is 3.4
kg⋅m2 when his arms are outstretched, and drops to 1.8 kg⋅m2 when
his...

In this example we see how a system can have constant angular
momentum without having a constant angular velocity! A physics
professor stands at the center of a turntable, holding his arms
extended horizontally, with a 5.0 kgkg dumbbell in each hand
(Figure 1). He is set rotating about a vertical axis, making one
revolution in 2.0 ss. His moment of inertia (without the dumbbells)
is 3.4 kg⋅m2kg⋅m2 when his arms are outstretched, and drops to 1.8
kg⋅m2kg⋅m2 when his...

Suppose a friend is completing another physics assignment in
their chair at their desk and you take the opportunity to turn this
scenario into the physics question you now must complete. Your
friend and chair have a combined constant moment of inertia of 5.4
kg m2, and the chair can freely rotate. Now your friend picks up
two solid bricks (each of mass 1.1 kg) they accidentally collected
from one of the campus buildings, and experiment with rotational
kinematics. Supposing...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 35 minutes ago

asked 36 minutes ago

asked 44 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago