The Great Mass of a Meter Stick Challenge

        It was a momentous day when Physics F Block walked into class and heard the words "I've got a challenge for you guys today," and a challenge it certainly was. After studying in class lessons on torque, rotational inertia and velocity, and the conservation of angular momentum, we were given the task to calculate the mass of a meter stick only using a 100g weight. Tricky right? My brain exploded just a tad. In my head I was thinking, "How on earth can I do this?!" Thankfully, my partner Margaret Anne had more of a cool head than I did (being a red head has disadvantages sometimes). We thought about the lesson we had just learned on torque, and got to work.
      So thinking about torque, we need to realize that it is equal to the force multiplied by the lever arm; the lever arm is a fancy way of saying the distance from the axis of rotation. We also know that torque causes rotation. Finally, we know that when an object is balanced, like say a see-saw, the counterclockwise torque is equal to the clockwise torque. Thinking this through, we decided that the best step would be to find the lever arm of the meter stick. So, we balanced the weight on the end of the meter stick, and pushed it toward the end of the desk until it was in a balanced state. The meter stick was level at twenty-two inches. We know that a meter stick equals one hundred centimeters, so we could therefore subtract twenty-two from 1one-hundred, and we got seventy-eight.
      Now it got a little tricky (like it hadn't already); we needed to find the lever arm of the other side of the meter stick. To do this, we needed to know the center of gravity, which on a meter stick will always be around fifty centimeters. From there, we subtracted fifty from seventy-eight, and got that the second lever arm would be twenty-eight centimeters. We had all the measurements we needed, but now we had to plug these numbers into an equation.
        As we said before, we know that when a meter stick is balanced (like it was) the clockwise torque is equal to the counterclockwise torque. This gave us an equation to plug our measurements into. Like we said before, we know that torque is equal to the force multiplied by the lever arm; accordingly, our equation became counterclockwise lever arm x force= clockwise lever arm x torque. We said the force on the first side was the weight, so we multiplied that by our twenty two centimeter lever arm. On the opposite side we multiplied our twenty-eight centimeter lever arm by our unknown force. Once we plugged the answer in, our unknown force was 78.57.
         We measured the meter stick and got around 83 grams, which is pretty close to our actual answer. While it was a tough process, it was interesting to use physics to way something without using a scale. It was a good way to wake up our brains in the morning.