Part One.
Experiment 9: Torque
TRIALS 1-7: You will check whether the torque calculated from τ = F l matches the torque actually measured by a torque wrench.
You have a wooden beam which pivots like a see-saw. For each trial, attach the torque wrench to its center, hang a weight from one of the pegs, and then hold the beam stationary by the handle of the torque wrench. If the hook on the weight is too short, hang a paper clip from the peg, and hang the weight from the paper clip. Record the reading on the torque wrench, which reads in inch-pounds.
The needle's reflection should be directly behind the needle itself, so you are looking directly at it.
On the answer sheet, record the weight in pounds and its lever arm in inches. Calculate the torque from the formula τ = F l
in the space on the right. Comment on whether the two values agree. (The wrench can be trusted to about ± 2 inch-pounds.)
1. Set up the apparatus so that a 1 pound weight makes a torque of 10 inch-pounds.
2. With the same force, make the torque 5 inch-pounds.
3. With the same force, make the torque 20 inch-pounds.
4. Use a 2 pound force to make a torque of 10 inch-pounds.
5. Use a ½ pound force to make a torque of 10 inch-pounds.
6. If you tip the beam, the force's lever arm gets shorter, as shown.
Use a 1 pound force on the peg 20 inches from the pivot (with no other weight on the beam) to make a torque of 18 inch-pounds. Use a string with a weight on the end to judge a vertical line through the 1 pound. Then measure the lever arm to the line of action, as shown.
(Measuring an angle then calculating is more work.)
7. With the same weight on the same peg, make the torque 15 inchpounds.
TRIAL 8: Now, use two weights instead of one, and eliminate the wrench. Set up the apparatus so that the beam balances with a 1 pound force on one side, and a ½ pound force on the other. Sketch the situation. What is the total torque on the beam?
Part Two.
You will check for conservation of energy, and also check Newton's second law of rotation, τ = Iα,

in the data from last week’s experiment with the metal disk. (No additional measurements are needed today.)
From last week’s lab, copy the distance which the disk fell, its mass and radius, the maximum and minimum radius of its axle, its initial and final angular velocity, and its angular acceleration.
Compute its moment of inertia, showing with your answer the formula used to find it.
Energy: Calculate E i,
the disk’s energy at the top, and E f,
the system’s energy at the bottom.
Assuming each of these to be good to + 10%, calculate their uncertainties. Note that the kinetic energy in this situation is primarily in the form of rotational kinetic energy.
(We are making two mistakes here, which approximately cancel each other: One is that the system actually starts out with more potential energy than you calculated, because you left out the mass of the axle assembly. The other is that we are not accounting for energy lost to friction on the way down.)
Torque: Compute the quantity Iα. Separately find τ, the torque causing the disk to rotate, and see if they match:
- Compute the weight of the disk. Because the disk's acceleration is small, this weight is nearly equal to the tension in the string, F.
- From F and the maximum and minimum radius, find the maximum and minimum torque of the string tension.
Conclusions: Does the initial energy agree with the final energy? Within τ’s range of uncertainty, does τ = Iα ?

PHY 121
Part One:
Trial
Reading on wrench
(in in
 lb)
1
2
3
4
5
6
7
8 Sketch:
F = l
=
F = l
=
F = l
=
F = l
=
F = l
=
F = l
=
F = l
=
Experiment 9: Torque
Measurements
Calculate τ from F and l
(in in
 lb)
Are they within
2 in
 lb?
Total Torque =

Part Two: h = ________________ M = _______________ R = _______________ r min
= ______________ r max
= ______________
ω i
= _______________
ω f
= _______________
α = ________________
I =
(KE + PE) i
=
(KE + PE) f
=
Iα =
Weight = F =
τ min
=
τ max
=