Center of Gravity and Rotational Inertia

This project is worth 10% of your overall grade for this course. Be sure to read all the instructions and assemble all the necessary materials before you begin. You will record your data and insert your answers on this project page. When you have completed BOTH parts of this project you may submit it electronically through the online course management system. Check the instructions in the online course for more information.

Part A: Finding the Center of Gravity of a Lever

In this activity you will work with weights and a lever to find the center of gravity and torque for different configurations. You will record your findings in the spaces provided. Feel free to add more space if you need it.

Materials you will need to complete this activity include a meter stick (or the equivalent), masses (10 washers), 50 cm of pulley cord, and a metric ruler.

Procedure:

Step 1: Find the center of gravity of a meter stick. (If you do not have a meter stick, use the metric ruler to make an equivalent instrument by placing markings at five or ten centimeter intervals.)

Step 2: Suspend the meter stick from the center-of-gravity point using 30-50 cm of pulley cord. Put the zero centimeter end of meter stick on the left.

Step 3: Hang five washers at the 25 cm mark. Record the distance from the fulcrum (the center of gravity in this case) to the washers.

Describe what kind of torque this set of five washers gives the meter stick.

Step 4: Balance the meter stick with five washers on each end. Record the distance from the fulcrum to the washers.

Describe what kind of torque this set of five washers gives the meter stick.

What is the net torque created by these two sets of washers?

Step 5: Replace the five washers added in Step 4 with three washers. Record the distance from the fulcrum to the washers.

What is the net torque created by these two sets of washers?

Step 6: Repeat the experiment with seven washers on the left of the fulcrum at the 25 cm mark and ten washers to the right of the fulcrum at the 75 cm mark.

Be sure to record the distance from the fulcrum to the washers.

What is the net torque created by these two sets of washers?

Step 7: Repeat the experiment with six washers on the left at the 30 cm mark. Record the location on the right-hand side where four washers balance the six washers.

What is the net torque created by these two sets of washers?

Step 8: Construct a table of your data. Put positive signs on distances that create clockwise torques and negative signs on distances that create counterclockwise torques.

Step 9: Use the data in your table to calculate the torques and formulate a rule about the torques.

Step 10: Devise a procedure to find the weight of an unknown mass. Describe what you did and your results.

Part B: Can Races

This activity is designed to test your understanding of rotational inertia by doing something fun!

For this activity you will need a ramp (a board with books as the support for one end will work just fine), 1 large and 1 small can with solid or non-sloshing contents (such as beans or cream-type soups), 1 can with liquid or sloshing contents (like chicken noodle soup), and 1 small empty can with both ends cut out to use as a cylinder.

Step 1: Make a ramp using a board with books as the support. Use an angle of approximately 10°.

Step 2: Assemble the required materials. Construct a table of the types of cans you use along with their contents and weights or sizes. Include any other information about your cans that you think might be relevant.

Test your understanding of rotational inertia by holding can races. Feel free to include pictures or illustrations of your can races.

Step 3: Run a trial to see if the small can of solid contents will beat the can with liquid contents down the ramp you have just made. First, write down your hypothesis:

Now do the trial and record the results of the race.

Explain your results.

Step 4: Run a trial to see if a large can of solids will beat a small can of solids down the ramp.

Write down your hypothesis:

Now do the trial and record the results of the race.

Explain your results.

Step 5: Run trials using the cylinder and the large can of solids; the cylinder and the small can of solids; and the cylinder and the can of liquids. Create a table in which you record your hypothesis for each trial, record the results of each trial, and explain the results of each trial.