# A2L Item 186

Goal: Problem solve with rotational dynamics

Source: UMPERG-ctqpe156 A
uniform rod is hinged to a wall and held at a 30° angle by a thin
string that is attached to the ceiling and makes a 90° angle to rod.
The tension in the string is 10N. The weight of the rod is about

1. 13N
2. 18N
3. 20N
4. 23N
5. 40N
6. none of the above

### Commentary:

(4) Some students will use the wrong trigometric function and
conclude that the weight is 40N.

An interesting follow up question is to ask what is the hinge force.
Students often forget that both the sum of the forces and the sum of the
torques must be zero for static equilibrium.

# A2L Item 185

Goal: Reasoning and hone the concept of torque.

Source: UMPERG-ctqpe152 A
uniform rod of length 4L, mass M, is suspended by two thin strings,
lengths L and 2L as shown. What is net torque about the left end of the
rod?

1. 0
2. 4MgL
3. 8MgL
4. 12MgL
5. None of the above

### Commentary:

(1) Since the rod does not rotate the total torque must be zero
about any point. Many students overworry this problem not realizing
that, independent of the angle of the rod, the other string is twice as
far as the center of mass of the rod.

# A2L Item 178

Goal: Problem solving with rotational dynamics

Source: UMPERG-ctqpe140 A disk
on a horizontal surface sits against a curb. A string wound around the
disk is attached to a mass as shown. If R=5 cm and h=2 cm, the largest
m for which the disk will not move is

1. Less than 2M
2. 2M
3. 3M
4. 4M
5. 5M
6. Greater than 5M
7. Cannot be determined.

### Commentary:

(4) When m = 4M the torques about the contact point between the disk and
curb balance. Students find this problem very difficult although rather
simple. Many have the most difficulty with the simple geometry needed to
find the moment arms.

# A2L Item 177

Goal: Problem solving with rotational dynamics

Source: UMPERG-ctqpe135.5 A
disk, with radius 0.25 m and mass 4 kg, lies on a smooth
horizontal table. A string wound about the disk is pulled with a
force of 8N. What is the angular acceleration of the disk about its
center?

1. 0
6. None of the above.
7. Cannot be determined

### Commentary:

(6) The correct value of αcm is 16 rad/s2. Students have the erroneous
concept of ‘conservation of force’. Many think that since the disk
moves, the full force cannot contribute to the torque about the center
of the disk.

# A2L Item 172

Goal: Hone the concept of torque

Source: UMPERG-ctqpe130 Given
F1 = 6N, and F2 = 8N, what is the total torque

1. 1.0 N-m, out
2. 0.7 N-m, in
3. 7.0 N-m, out
4. 1.0 N-m, in
5. 6.0 N-m, out
6. None of the above.

### Commentary:

(6) Many students use the origin rather than the point A. This provides
the opportunity to stress that torque is found with respect to a
specified point. Students using the right hand rule incorrectly may

# A2L Item 103

Goal: Reason with rotational dynamics.

Source: UMPERG-ctqpe138 A spool has string wrapped around its center axle and is sitting on a
horizontal surface. If the string is pulled at an angle to the
horizontal when drawn from the bottom of the axle, the spool will

1. roll to the right.
2. not roll, only slip.
3. roll to the left.
4. cannot be determined.

### Commentary:

(4) The motion of the spool depends upon the angle θ. When the line of
action of the force passes through the contact point the spool will
slide and not rotate. At lower angles it will roll to the right and at
higher angles it will roll to the left.

# A2L Item 104

Goal: Hone the concept of torque

Source: UMPERG-ctqpe131 1. There are no points having zero total torque.
2. There is one point having zero total torque.
3. There are many points having zero total torque.

### Commentary:

(3) Many students realize that there is at least one point, the
intersection of the lines of action of the two forces, having zero
torque. A drawing is usually sufficient to convince students that there
is an entire line along which the torque is zero.

# A2L Item 101

Goal: Reason with rotational dynamics.

Source: UMPERG-ctqpe136 A spool has string wrapped around its center axle and is sitting on a
horizontal surface. If the string is pulled in the horizontal direction
when tangent to the top of the axle, the spool will

1. roll to the right.
2. not roll, only slip.
3. roll to the left.
4. cannot be determined.

### Commentary:

(1) For many students this remains counterintuitive.

# A2L Item 102

Goal: Reason with rotational dynamics.

Source: UMPERG-ctqpe137 A spool has string wrapped around its center axle and is sitting on a
horizontal surface. If the string is pulled in the horizontal direction
when tangent to the bottom of the axle, the spool will

1. roll to the right.
2. not roll, only slip.
3. roll to the left.
4. can’t be determined.

### Commentary:

(1) For many students this is really counterintuitive.

# A2L Item 097

Goal: Hone the concept of torque.

Source: UMPERG-ctqpe150 A uniform rod of length L, mass M, is suspended by two thin strings.
Which of the following statements is true regarding the tensions in the
strings?

1. T2 = T1
2. T2 = 2.5T1
3. T2 = 0.6T1
4. T2 = 0.8T1
5. None of the above