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?