How to find the mass of a meter stick without using a scale!

If a meter stick was not balanced on the edge of a table had a torque, what would it look like?
                                       
                          |____| <-- level arm
           --------------------------- <-- meter stick
                           |       /\ <-- center of gravity
                           | <-- force
This meter stick has a counter clockwise torque, moving to the left. The level arm is placed between the force and the center of gravity.

Now the meter stick is balanced on the edge of the table. What do you know about the relationship between the edge of the table and the center of gravity?
           |  <-- Force
_____ |___________________
           |  /\
           | <-- Force       
Force goes up the same amount it is being pulled down. For an object to be balanced, the object on wither side of the center of gravity must have the same mass. The Counter clockwise and clockwise torque must be equal.


Now watch how the balance point changes when the 100g mass is added to the end of the meter stick. Draw a picture and label the forces and level arms that are causing the clockwise and counter clockwise torques.
     100 g
     _____________________
            /\
The center of mass of the meter stick does not change, but the center of gravity does in order to balance out the added weight.

When we first began to plan out how to find the mass of the meter stick, we were beyond confused!!! To get started, we found where on the meter stick the stick was balanced with the 100 g weight on the end of the stick. We found that it was balanced at 29.5 cm.
In order to convert our 100g into mass we move the decimal to the left one place to get .1 kg.
9.8 is gravity and to convert that, we move the decimal over one place to the left as well.
In order to find the mass of the meter stick, we need to use the angular momentum equation which is, (level arm)(force) = (level arm)(force)
           before                         after
And to find the official mass, we use the equation w=mg

Now to solve,
29.5 cm = .295m
(29.5)(.98) = (20.5)(force)
28.91 = 20.5x
------     -------
20.5      20.5

x = 1.41 N

w=mg
1.41=m(9.8)
-----  --------
9.8      9.8

m= .143 kg 

When trying to figure out how in the world we would find the mass of the meter stick, we stared long and hard at it. We found the center of mass of the meter stick which was 50 cm and then the mass of gravity with the weight on it which was 29.5cm. A key detail that we learned was that just because we added the weight to the stick, the center of mass of the meter stick DOES NOT CHANGE. For the meter stick to be balanced, there must be a counter clockwise and clockwise torque that are equal. The lever arms are located where the center of gravity is to the downward force, and then from the center of gravity to the weight at the end of the stick. The mass we calculated was .143 kg and the real mass was .142 kg.
                                 .3m            .2m
                              ____________________
                              |         |                              |
____________________________________
                              |         /\                            |
             --> 50 cm |                                        |  <-- .98 N  Gravity
                   Center of mass