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.
Goal: Hone the concept of angular velocity and link to rotational inertia and angular momentum
Source: UMPERG-ctqpe122
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. As a result of dropping the rock,
what happens to the angular velocity of the child and disk?
Answer
(2) is the correct response if the rock is simply dropped. However, some
students selecting this choice may think that the angular velocity is
maintained by some external agency. Students selecting answer (1) are
likely misapplying conservation of angular momentum.
Background
This question is useful for revealing whether students understand the
concept of moment of inertia and its relationship to angular momentum.
Many students reason that after the rock is dropped, the moment of
inertia is smaller and the angular velocity must increase to conserve
angular momentum.
RevealingQ
When dropped, does the rock have angular velocity? Just before being
dropped does the rock have angular momentum? Just after being dropped
does the rock have angular momentum?
Suggestions
It is possible to do a traditional demonstration of the role of moment
of inertia in angular momentum and then just drop the weights when arms
are extended.
Goal: Understanding the first law.
Source: UMPERG-ctqpe120
A
child is standing at the rim of a rotating disk holding a rock. The
disk rotates without friction. If the rock is dropped at the instant
shown, which of the indicated paths most nearly represents the path of
the rock as seen from above the disk?
(2) is the correct path if the rock is simply dropped. Some students
selecting answer (3) may be viewing the rock from the child’s
perspective. Some students indicating choice (5) may interpret this
path as ‘straight down’.
This question is similar to others which seek to reveal student
perceptions about path persistence. It is a slightly different context
from the purely horizontal case of a ball rolling on a horizontal
surface around an semicircular section of hoop.
What path would the child see?
What is the velocity of the rock just before it is dropped? just after?
What would the path of the rock have been if the child continued to hold
it?
There are a variety of demonstrations that can be done as followup to
this question. It is important that students perceive the similarity
between the demonstration context and the problem situation.
Goal: Honing the concept of acceleration especially regarding circular motion.
Source: UMPERG
A child is swinging. What is the direction of her acceleration when the
swing is at its lowest point?
(1) The acceleration is in the upward direction. The child is traveling
in a circle and at the lowest point the acceleration is all radial.
Circular motion must have been covered for the item to be of use. The
question may be answered using either kinematics or dynamics. The
direction of the acceleration can be realized using kinematics by
drawing the velocity vector just before the lowest point and just after
the lowest point. The difference is proportional to the acceleration
and this difference points toward the center of the circle. At the
lowest point all forces are vertical so the acceleration must also be in
the vertical direction. The tension is larger than the weight so the
acceleration is in the upward direction.
What is the definition of acceleration? What is the direction of the
velocity of the child when at the lowest point of the swing? Is it
getting larger or smaller? Is it changing direction? What forces act
on the child at the lowest point of the swing and in what direction are
these forces?
Have students draw a motion plot indicating the position and the
velocity vector of the child at various points in the child’s motion.
Do their drawings reflect that the velocity is always tangent to the
circular path, but increasing in magnitude as the child swings toward
the lowest point?
Commentary:
Answer
(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.