# A2L Item 173

Goal: Hone the concept of angular momentum

Source: UMPERG-ctqpe132

Which situation has the least (magnitude) angular momentum about the
origin?

1. A 2 kg mass travels along the line y = 3m with speed
1.5 m/s.
2. A 1 kg mass travels in a circle of r = 4.5 m about the
origin with speed 2 m/s.
3. A disk with I = 3 kg-m2
1. A
2. B
3. C
4. Both A and B
5. Both A and C
6. Both B and C
7. All have the same magnitude angular momentum

### Commentary:

(7) Students frequently think that objects traveling in a straight line
have no angular momentum. An interesting follow up question is to ask
how students would answer if the disk in situation were rotating about
the point (1,0).

# A2L Item 080

Goal: Problem solving using conservation of angular momentum.

Source: UMPERG

A bug walks on a freely rotating disk. Given: Mbug=0.05 kg,
Idisk=0.03 kg-m2, Rdisk=0.5 m, and
ωo= 2 rad/s when bug is 0.1 m from center. The bug
crawls to 0.4 m from the disk’s center. The final ω is most
nearly:

6. None of the above
7. Cannot be determined

### Commentary:

(1) This is a very traditional conservation of angular momentum problem.
The only difficulty is due to the presence of extraneous information.
Some students may use conservation of energy.

# A2L Item 081

Goal: Develop a strategic approach to problem solving.

Source: UMPERG

A bug walks on a rotating disk. Given: Mbug,
Idisk, Rdisk, and ωo when the bug
is at r1. The bug crawls to r2. Find
ωfinal for the system.

What principle would you use to solve the problem MOST EFFICIENTLY?

1. Kinematics only
2. F = ma or Newton’s laws
3. Work-Energy theorem
4. Impulse-Momentum theorem
5. Angular Impulse-Angular Momentum theorem
6. Not enough information given

### Commentary:

(5) This problem helps students develop a principle-based approach to
problems. Many students may think correctly that this is a conservation
of angular momentum problem and not recognize that the general principle
is the angular impulse – angular momentum theorem.

# A2L Item 069

Goal: Problem solving.

Source: UMPERG-ctqpe146

A
child having mass 32kg is standing at the rim of a rotating disk of
radius 1.5m. The disk is free to rotate without friction. The disk has
moment of inertia I = 125kg-m2 and is initially at rest. The
child throws a rock of mass 4kg in the forward tangential direction as
shown in the figure with a speed of 5m/s. The final angular speed of
the disk is most nearly

8. None of the above
9. Cannot be determined

### Commentary:

(7) is the most appropriate response. Initially there is no angular
momentum in the system. The child and disk must rotate clockwise to
balance the angular momentum of the rock. Some students may forget to
add the moment of inertia of child to that of the disk.

#### Background

Throwing the rock tangentially gives the rock angular momentum relative
to the fixed center of the disk. The disk-child system must have an
angular momentum which is the negative of that of the rock. Thus, it is
possible to find the angular velocity. The angular velocity is
negative, i,e, into the page.

#### Questions to Reveal Student Reasoning

Does the total system have angular momentum just before the rock is
thrown? just after it is thrown?

Does the rock have angular momentum just before it is thrown? just
after it is thrown?

What happens to the child upon throwing the rock? Does the child move?
How?

#### Suggestions

Have students relate their answer to this question to items 67 and 68.

# A2L Item 068

Goal: Problem solving and developing strategic knowledge.

Source: UMPERG-ctqpe145

You are given this problem:

A
child is standing at the rim of a rotating disk holding a rock. The
disk rotates without friction. The rock is thrown in the RADIAL
direction [path (5)] at the instant shown. You are given:

• Mass of the child
• Mass of the thrown rock
• Velocity of the rock
• Initial angular speed of the system

You want to find the final angular speed of the disk and child.

What principle would you use to solve the problem MOST EFFICIENTLY?

1. Kinematics only
2. F= ma or Newton’s laws
3. Work-Kinetic Energy theorem
4. Impulse-Momentum theorem
5. Angular Impulse-Angular Momentum theorem
6. More than one of the above
7. None of the above
8. Cannot be determined

### Commentary:

(5) is the correct response if the rock is thrown radially. Since there
is no angular impulse, there can be no change in angular momentum.
Neither the rock alone, nor the child/disk system changes angular
momentum.

#### Background

Throwing the rock radially, clearly increases the kinetic energy but not
the angular momentum. Consequently, the final angular speed of the disk
and child is the same as the initial speed.

#### Questions to Reveal Student Reasoning

Does the rock have angular momentum (or energy) just before it is
thrown? just after it is thrown?

If energy (angular momentum) is gained, where does it come from?

Changes in angular momentum are caused by a net torque. What torques
act on the system during the process of throwing?

#### Suggestions

Have students relate their answer to this question to item 67.

# A2L Item 065

Goal: Recognize physical conditions under which conservation principles hold.

Source: UMPERG-ctqpe134

A
child is standing at the rim of a rotating disk holding a rock. The
disk rotates without friction. The rock is dropped at the instant
shown. What quantities are conserved during this process.

1. Only angular momentum is conserved.
2. Only mechanical energy is conserved.
3. Both angular momentum and mechanical energy are conserved.
4. Neither is conserved.
5. cannot be determined.

### Commentary:

(3) is the correct response if the rock is simply dropped. Some
students may fail to include the rock as part of the system after it is
dropped.

#### Background

Objects traveling in a straight line do have angular momentum with
respect to any origin that is not on the path of the object. The rock
does not cease to have angular momentum with respect to the center of
the disk when it is dropped. Although the angular momentum and energy of
the rock will change as the rock falls, its angular momentum and energy
just after it is dropped are the same as just before.

#### Questions to Reveal Student Reasoning

Does the rock have angular momentum (or energy) just before it is
dropped? just after it is dropped?

If energy (angular momentum) is lost, what happens to it?

Changes in angular momentum are caused by a net torque. What torques
act on the system?

#### Suggestions

Have students relate their answer to this question to the previous one.