PHYS 1401 – General Physics I
Moment of Inertia
Leader:
___________________ Recorder:
__________________________
Skeptic:
___________________ Encourager:
________________________
Materials
Torque
feeler at instructor’s desk w/ mass hanger and gram mass set
Spring
Scale, Green (5 N capacity)
Pasco
Rotational Motion Apparatus with rotating platform attached
Stop
watch
Introduction
In this lab we will examine two
things. First, we will review the idea
of torque introduced in the previous lab.
Second, we will examine the effect of applying a constant torque
Part I Review of Torque
For
this part of the activity there is one set up at the instructor’s desk. Each group should take a turn completing this
part of the activity. While waiting for
your group’s turn, you can continue this activity beginning at part II below.
In
this part of the activity you will use a device called a “torque feeler”. A torque feeler is a handle attached to a rod
from which masses can be hung at different distances. You hold the handle with both hands, one on
either side of the rod, with palms facing down.
In our case the “rod” is actually a meter stick. A mass hanger is hung from a clamp on the meter
stick.
Procedure
Move
the clamp to the 50 cm mark on the meter stick and hold the torque feeler so
that the rod is horizontal. While
supporting both ends of the torque feeler, suspend the mass hanger from the
clamp and place an additional 150 g on the mass hanger. Support the handle with your closed hands but
do not grasp the handle firmly, instead allowing the handle to rotate in your
hand. Release the side of the torque
feeler opposite the handle and observe the subsequent motion. You can remove the additional mass from the
mass hanger.
Q1) Describe the motion of the torque
feeler. Did it fall straight down, did
it move diagonally, swing on an arc, etc.?
In this case, the weight exerts a force
that causes the torque feeler to speed up along an arc of circle. A force applied this way produces a torque.
Q2) Did the angular velocity of the torque feeler
change?
Q3) If the answer to Q2) was yes, then the torque
feeler had and angular _______.
Now
grip the handle firmly and hold the rod horizontally with the mass on the
hanger. Now that you are not allowing the handle to rotate so you are also
exerting a torque on the torque feeler
Q4) How does the torque you exert compare to the
torque exerted by the weight? Explain.
While
holding the torque feeler horizontally, add an additional 100 g to the mass
hanger.
Q5) Do you feel a change in the torque you have
to exert when you add the extra 100 g?
Add
another 100 g.
Q6) Do you feel a change in the torque you have
to exert when you add the extra 100 g?
Add
another 100 g
Q7) Do you feel a change in the torque you have
to exert when you add the extra 100 g?
Q8) As the force applied by the weight goes up,
how does the torque change (bigger, smaller, no change)?
Replace
the mass hanger with the 500 g mass on the hook. Feel the torque you have to apply to hold the
torque feeler horizontal. Now move the
clamp so that it is 10 cm from the handle.
Again, hold the torque feeler horizontally.
Q9) Is the torque you have to exert as big as
when the mass hanger is 10 cm form the handle as when it was in the middle of
the rod?
While
holding the torque feeler horizontally, move the clamp holding the 500 g mass
out in 10 cm increments. Stop after each
increment to feel the torque. Continue until the clamp reaches the end of the
stick.
Q10) As the weight is moved away from the handle,
how does the torque change? (bigger,
smaller, stays the same)
Up to
this point we have investigated how the torque depends on the force creating it
and how it depends on the distance from the handle that it is exerted. There is one more factor that affects torque.
Start
with the rod held horizontally and with the 500 g mass hanging from near the
end of the rod. Slowly rotate your
wrists back so you raise the end of the torque feeler. Continue until the torque feeler is almost
vertical.
Q11) As you rotate the end of the torque feeler
up, how does the torque that you have to apply change?
When
you hold the rod horizontally, the angle between the rod and the weight is
90°. When the rod is almost vertical,
the angle between the rod and the weight is about 0°.
Q12) The torque is maximum when the angle is
_____, and the torque is minimum when the angle is _______.
Summary Questions for Part I
S13) As the weight of the hanging mass increases,
what effect was there on the torque exerted by the weight.
S14) As the distance the mass was located from the
handle increased, what effect was there on the torque exerted by the weight?
S15) As the angle between the meter stick and the
weight decreased, what effect was there on the torque?
Part II – Moment of Inertia
In this part of the lab we
will investigate rotational inertia. For
motion in a line, inertia is determined by the mass. We will investigate the factors that affect the
resistance to change in rotational motion.
Procedure
The rotating platform has
masses that can be slid. Loosen the wing
nuts and slide both masses so that they sit next to each other with their inner
edges sitting on the 0 cm mark.
Wind up the string around the
largest of the three wheels below the rotating platform. Hook the spring scale on the loop at the end
of the string. Hold the platform and
pull on the spring scale so that it reads 2 N.
Release the platform and pull on the string so that you maintain a
constant force of 2 N. You may need to
practice this several times. Once you
can pull with a fairly steady force of 2 N, then starting from rest, use the
stopwatch to time 3 complete revolutions of the apparatus pulling the entire
time with a constant 2 N force.
Q16) Record the time.
Q17) If the force is constant, then what will be
true about the applied torque in this case?
Q18) What is the initial angular velocity for this
situation?
Q19) What is the angular displacement?
Q20) Assuming that it is constant, determine the
angular acceleration for this situation.
show your work in the space below.
Now loosen the wing nuts and
move each mass so that its inner edge now sits at the 10 cm mark on the
rotating platform. Tighten the wing nuts
again.
Q21) Did you change the amount of mass on the
platform?
Q22) If you wind the string around the same wheel
and apply a 2 N force again will the torque change from your first trial? Explain.
P23) Predict if the angular acceleration will be
the same, less or greater if you conduct the same procedure as before.
Repeat the same procedure as
before.
Q24) Record the time for this trial.
Q25) Determine the angular acceleration for this
trial.
Now loosen the wing nuts and
move each mass so that its inner edge now sits at the 20 cm mark on the
rotating platform. Tighten the wing nuts
again.
Q26) Did you change the amount of mass on the
platform?
Q27) If you wind the string around the same wheel
and apply a 2 N force again will the torque change from your first two
trials? Explain.
P28) Predict if the angular acceleration will be
the same, less or greater if you conduct the same procedure as in the previous
trial.
Repeat the same procedure as
before.
Q29) Record the time for this trial.
Q30) Determine the angular acceleration for this
trial.
Q30) Did the amount of mass on the platform change
in this experiment?
Q31) As the distance from the
axis that the mass was located increased, what happened to the angular
acceleration.
Q32) Not only mass affects rotational inertia, but
also where it is located. What effect is
there on the resistance to changes in rotational motion by placing the mass
further from the axis? Cite specific
evidence from this experiment to support your answer.