Torsion Pendulum

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Motor Hanging on pendulum
Rocket on Pendulum

 

Goal:

A torsion pendulum can measure the Moments of Inertia of an object. Since we needed to measure our rocket's moment of inertia for the ASU project, we built one.

How a torsion pendulum works:

Rather than repeat what I learned from the web, I'll provide links to helpful web pages.

http://www.upscale.utoronto.ca/IYearLab/Intros/TorsionPend/TorsionPend.html

http://farside.ph.utexas.edu/teaching/301/lectures/node139.html

Equipment:

  • High tensile strength steel wire - we used .018" dia music wire.
  • Motor Nozzle Disc - This device replaces the nozzle of a 54 mm high power rocket motor. The Nozzle O-ring secures it in place so that its orientation is locked to that of the motor and rocket. See the drawing and picture below.
  • The upper bracket - This bracket secures the wire to a roof rafter. See picture below.
  • Calibration Mass - A 5.5" dia. x 10" solid aluminum cylinder was used as a calibration mass to determine the wire constant.

Gallery:

Click on the thumbnail image to see a high resolution image.


Nozzle Disc


Nozzle Disc Installed

Calibration Mass


Top Bracket


Top Bracket Wire Fastener

Measurement:

First we measured the mass of the Calibration Mass, calculated its Roll Moment of Inertia., then mounted it on the pendulum. We measured the length of a minimum of ten oscillations. This permitted the calculation of the wire constant.

The keeping the wire length the same, we replaced the Calibration Mass with the rocket. The rocket was prepared as if for launch, except that the motor nozzle and propellant grains were omitted. The nozzle was replaced with the Nozzle Disc, so the rocket could be hung in the pendulum. The propellant was omitted, because we wanted to determine the rocket's moment of inertia during the coast phase of the flight (after the propellant is consumed).

Video of pendulum

Results:

Calibration weight
Time from Video Camera
Cycle Min Sec Frame Total Time Period
0 0 24 7 24.2333
1 1 4 7 64.2333 40.0000
2 1 43 26 103.8667 39.6333
3 2 23 21 143.7000 39.8333
4 3 3 18 183.6000 39.9000
5 3 43 13 223.4333 39.8333
6 4 23 7 263.2333 39.8000
7 5 3 5 303.1667 39.9333
8 5 42 27 342.9000 39.7333
9 6 22 21 382.7000 39.8000
10 7 2 20 422.6667 39.9667 398.4333
middle times are approximate
Average 39.84333 39.84333 Period
Mass 8.8 Kg Iz= 0.017725 Kg*m^2
Diameter 126.94 mm
Radius 0.06347 m Wire Constant 0.0001403
Wire dia 0.018 in
Wire Len 0.71755 m

Rocket prepared for launch*.

Rocket with K480W (no propellant)
Time from Video Camera
Cycle Min Sec Frame Total Time Period
0 1 59 6 119.2000
1 2 39 23 159.7667 40.5667
2 3 20 10 200.3333 40.5667
3 4 1 10 241.3333 41.0000
4 4 42 23 282.7667 41.4333
5 5 24 3 324.1000 41.3333
6 6 4 1 364.0333 39.9333
7 6 45 8 405.2667 41.2333
8 7 26 17 446.5667 41.3000
9 8 8 2 488.0667 41.5000
10 8 49 16 529.5333 41.4667
11 9 29 13 569.4333 39.9000 450.2333
middle times are approximate
Average 40.9303 40.9303 Period
Mass 7.83 Kg Iz= 0.018705 Kg*m^2

In the future we plan to also measure the rockets other moments of inertia..