The Inertial Balance


To use an inertial balance to measure the masses of objects.


"Mass: The quantity of matter in a body. More specifically, it is a measure of the inertia or "laziness" that a body exhibits in response to any effort made to start it, stop it, or change in any way its state of motion."1

There are several ways to measure mass - a triple-beam balance measures mass, for instance. The triple-beam balance has a couple of disadvantages, however. First, it is difficult to see how the measurement you make on a balance correlates to the definition of mass given above, and the triple-beam balance won't work where there is no gravity.

If mass measures the "laziness" of an object in response to efforts made to change its velocity, it makes sense that you should be able to measure mass by making an effort to change the velocity of an object and recording its "laziness." This is what an inertial balance does. It uses two strips of spring steel to apply the same "effort" in order to vibrate it back and forth. (A vibration involves speeding up, slowing down, and changing direction, so the state of motion of the object is certainly changed.) If the object vibrates quickly it is not "lazy" - it does not have much mass. Objects that vibrate slowly have a large mass.

When its resistance to a change in motion determines the mass of an object, the mass is called the inertial mass and it is measured with an inertial balance. The inertial balance is actually 2 pans connected by two flexible, metal blades. One pan is clamped to a table and the other is allowed to vibrate horizontally. The time for one complete back-and-forth motion is called the period (T). The period depends upon the stiffness of the blades and upon the mass in the vibrating pan. Masses and periods are related according to the equation:


Where m1 & m2 are different masses, and T1 & T2 are their respective periods. Since the blades vibrate horizontally, the measured inertial mass is independent of gravity which works in the vertical.


  1. Each person in your lab group must read every page in this online procedure. Along the way, there will be questions that you must answer.
  2. Designate one person in your group as the Data Recorder. This person should open the Google document Experiment 1 - Inertial Balance for the approved answer template.
  3. When this Google document opens, sign in to your Google account.
  4. From theFILE Menu, chooseMake a copy...
  5. From theFILE Menu, chooseRename...and rename the document as follows: Exp 1 - Period (1, 3, 6, or 8) - Group #.
  6. Share this document with the members of your group and with Mr. Skubis at
  7. As a group, answer all questions. Remember to use complete sentences and be mindful of grammar, spelling, and punctuation.
  8. Finally, AS A GROUP write a CONCLUSION as described at the end of this lab. Submit the conclusion on the Google document for full credit.
  9. REMEMBER: **Plagiarism** is a form of **Academic Dishonesty** which carries harsh consequences. DO YOUR OWN WORK!

Part 1 – Calibrating the Balance

  1. Clamp one end of the balance to the table so that the other end can oscillate freely in the air beside the table. When you place objects in the balance pan, you will need to use small pieces of masking tape to keep them from sliding about in the pan.

  2. Tape 600 grams (500-gram + 100-gram masses) to the free end of the balance and pull the free end about 4.0 cm away from equilibrium and release. The balance should oscillate smoothly after released. Note: if the original displacement is too large and the oscillations are inconsistent, the results of the experiment may not meet expectations.

  3. After becoming accustomed to the motion of the balance, use a stopwatch to determine the total elapsed time for 20 complete oscillations of the balance. Generally, because of reaction time error, it is not recommended to start timing when the balance is initially released. An oscillation must be a complete round trip, regardless of the starting point. Start counting the oscillations with “zero.” Record the results in your Google doc.

  4. Repeat the timing procedure until you have three time values for this mass. Later you can compute the average of the three values and use this number to determine the period.

  5. Repeat the timing measurements for additional masses on the platform, decreasing by 100 grams each time until 100 grams has been used.

Part 2 – Determining Unknown Inertial Masses

  1. Obtain 2 unknowns from your instructor and repeat the experiment with each. Record your results.

  2. Finally, determine the gravitational mass of the unknowns using the electronic pan balance. Record these results.


  1. Find the average period (T) for each calibration mass. Do the same for the unknowns. The average period is the average time divided by 20 oscillations. (Be mindful of sig figs.)
  2. Calculate T2 for each result.


Using only the data for the known masses, construct a graph of mass versus period-squared (T2 on the abscissa and mass on the ordinate) using Microsoft Excel. Mass should be in units of grams and period2 in units of s2. Create a line of best fit (see Excel instructions).
Have Excel display the resulting graph’s equation and correlation coefficient.

Note: Since you used an Excel spreadsheet for the graph, you do not need to show how the slope and y-intercept of the graph are determined. Excel will provide that information. However, any results calculated from these values should be included in sample calculations.

Plug your calculated T2 for the unknowns into the slope equation to find the inertial mass in each case. See your instructor for additional help if you need it.