PHY 1053L & 2048L Laboratory
Torque and Angular
Momentum
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Objective
The purpose of this lab is to determine torque and angular momentum of a heavy rotating disk,
wooden gears and levers, and to analyze the flow of energy related to rotational motions and to
understand the concept of forces and torques to balance simple mechanical machines.
Background
In this lab, gravitational forces and gravitational potential energy are the causes for rotational
motions. The lab consists of two experimental setups: A) a heavy iron disk, which is accelerated
by a weight on a string, and B) wooden gears and levers, where angular momentum on the lever
is transmitted via gears to another lever, we measure the forces, which keep the system in
equilibrium.
Mechanical advantage is a measure of the force amplification achieved by using a tool,
mechanical device or machine system. For a lever, the mechanical advantage is defined as the
ratio of the two lever arms:
For a set of two gears, the mechanical advantage is defined as the ratio of the two gear
diameters:
For a set of more than two gears, or a complex machine consisting of levers and gears, the
mechanical advantage is computed from each of the components of the mechanical system, or
mechanism.
Instructions Part A) Heavy Iron Disk
1) Begin rotating the disk by hand to get a feel of the force needed to set the disk in motion.
Lay the white wireless force/acceleration sensor flat inside the iron disk. Connect the
Capstone program to the sensor and measure angular velocity. Move again the disk by hand
and confirm Capstone shows the expected angular velocity. Ensure that the rotation of the
disk is correctly reflected in the data taken by the computer.
2) Measure the diameter of the disk. Write down the radius of the disk, including an error
estimate for the accuracy of your measurement.
Radius: ________________
MA = ra
rb
MA = da
db
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3) Hook one end of the string to the small magnet outside the rotating base of the disk and a
100 g weight to the other end. If the magnet slips use two or three. Turn the disk to wind
the string onto the disk, and observe at the same time how the weight on the other side of
the string lifts off the ground. Stop before the weight touches the pulley at the top end of
the rail. This is best done if one lab partner watches the weight, and another lab partner
handles the string around the iron disk.
4) Measure the distance from the top position of the weight to the position when the weight is
on the ground. (Estimate how well you can measure the difference, h, i.e. the change of
height of the weight. Keep in mind that this will determine how accurate you will be able to
determine the energy, which is available to set the disk in rotation!)
5) The first measurement is the angular velocity w(t) of the disk as function of time t, beginning
at the time when the disk is released with the weight at the topmost position, during phase
one with the weight moving downward to the ground, and during phase two with the
weight sitting on the ground, and the disk spinning at least ten times. (Ensure that the data
taken by the computer reflect exactly what you expect what is happening. If in doubt,
repeat and eliminate unrelated effects, or ask your instructor.)
6) Save your data set w(t) taken with a weight with the mass of 100 g. Check again if your data
set shows both, the acceleration phase and the free rotation phase clearly.
7) Repeat the measurement of w(t) with an driving mass of 200 g, and then 300 g. Save your
measurement. You should have now three data sets w(t) for the three different weights, 100
g, 200 g, and 300 g. Ensure those data set reflect exactly what you expect.
Instructions Part B) Wooden Gears and Levers
8) You have three sizes of gears. Attach the largest of the gears at about the height of your
eyes to the stand. Rotate the gear to the position where the zero degree marker points
vertically upward. Write down the number of teeth of the gear.
n(large): ___________
9) Attach the medium size gear below the other gear. With the top gear held in position, the
zero degree arrow of the bottom gear should point approximately vertically upward. Write
down the number of teeth of the medium gear.
n(medium): ____________
10) Turn the larger gear in one direction, and observe the smaller gear, and stop when the
smaller gear has completed one rotation. How many degrees did the larger gear rotate?
θ(1): _____________
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11) How many turns does the smaller gear complete, when the larger gear completes one
rotation?
n(turns): ____________
12) Attach a lever to the smaller of the two gears. Hang the force sensor in the hole labeled “30
cm” on one side of the lever, and a 500 g weight in the 30 cm hole on the other side.
Measure the force needed to balance the lever. Enter your measurement in Table 1 below.
13) Now move the weight from the 30 cm position to the 20 cm position. Measure the force
(still at the 30 cm hole on the other side) with a weight of 500 g and then of 1000 g needed
to balance the lever. Enter your measurement in Table 1 below.
14) Repeat the above, however, now with the weight attached to the 10 cm hole of the lever,
and measure the two forces needed to balance. Write down the number of teeth for both
gears.
n(medium): ____________
n(large): ____________
Table 1.
a) One Lever 30 cm 20 cm 10 cm
500 g
1000 g – – – –
15) Attach the second lever to the other gear – students may need to share levers between the
different stands. Let’s call the lever attached to the large gear the “large lever”, and the
other the “small lever”.
16) Hang the force sensor first into the hole labeled “30 cm” of the larger lever, and hang a 500
g weight (consisting of the holder with 50 g and a 500 g cylinder) into the 30 cm hole of the
small lever on the same side from the post. Measure the force needed to balance the two
levers.
17) Move the 500 g weight from the 30 cm hole of the small lever to the 20 cm hole. Measure
the force needed to balance. Is it larger or smaller or equal to the above?
18) Add another 500 g weight to the weight in the 20 cm hole. Measure the force needed for
balance.
19) Move the weight to the 10 cm hole of the small lever. Measure first the force needed to
balance a weight of 500 g, and second the force needed to balance 1000 g. Write down the
number of teeth of both gears.
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n(medium): ____________
n(large): ____________
Table 2.
b) 2 Levers, med 30 cm 20 cm 10 cm
500 g
1000 g – – – –
20) Remove the smaller of the gears, and replace it with the smallest gear. Attach the lever to
this gear as well.
21) Repeat the experiment b) 2 levers, largest gear and smallest gear. Measure all the forces
needed to balance 500 g and 1000 g attached to the 30 cm, 20 cm, and 10 cm holes of the
large lever. Write down the number of teeth for both gears.
c) 2 Levers, sml 30 cm 20 cm 10 cm
500 g
1000 g – – – –
22) Review your measurements and check them for reasonability. Do your results reflect what
you expected. Discuss with your group each setup.
Instructions Part C) Results for Iron Disk
23) Determine the gravitational force of the weight pulling on the string.
24) Compute the change of gravitational potential energy of the weight between the position at
the top and the position on the ground.
25) What is the force applied to the disk? Compute the torque applied to the disk during the
acceleration phase for the three different weights.
26) From your data sets w(t) of the rotating disk, determine the point in time between the
acceleration phase and the phase of free rotation.
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27) Evaluate the angular velocity during the phase of free rotation. Determine the maximum
angular velocity for each of the three weights.
28) What is the maximum frequency of the rotation? What is the period of revolution? What
can you derive for the change of those two quantities during the phase of free rotation?
29) What is the maximum angular momentum of the disk? Show your result in a table: The
three masses used to accelerate the disk in the first column, the maximum angular
momentum of the disk in the second. Make a graph of this data set.
30) Under the assumption that there is no energy loss in the motion of the string through the
pulleys, the gravitational potential energy of the weight is transferred to the kinetic energy
of the disk. Compute the moment of inertia of the disk.
Instructions Part D) Results for Gears and Levers
31) Compute the mechanical advantage for each of the gear sets you have used during the lab.
32) Compute the torques from the data taken in the above tables a), b), and c) for each of the
conditions.
33) Explain how each time you achieved mechanical balance by applying a certain force as
measured with the force sensor. Compare and discuss the quantity of the measured force
with the gravitational force of the weight in each position.
34) What did you learn in this lab?