Mass of Meter Stick

In class we were asked to find the mass of a meter stick by only using a meter stick and a 100g lead weight.

In this picture, the meter stick is balanced, so that means the torques are equal. The counter-clockwise torque equals the clockwise torque, because torque = (force)(lever arm)

In this picture, there is a 100g weight on the far side of the meter stick. The center of gravity stays the same, and the axis of rotation stays the same. The only thing that has changed is...

This picture demonstrates how to solve for the mass of the meter stick. We know gravity (9.8), the mass of the weight (100g or 1kg), how long the stick is (100m), the center of gravity (50m), the axis of rotation (70m) and the lever arms (20m and 30m). 50 is just the remaining mass of the meter stick, but it is not necessary to use in the equations for solving.

To solve for the mass of the meter stick, we first need to have to correct measurements. We know that the weight is 100g or 1kg, but weight is measured in Newtons so we need to do a conversion. 

w=mg

w=(.1)(9.8)

w=.98N

So we now know that the weight weighs 9.8N, and we can use that information in our equation.

torque = (force)(lever arm)

counterclockwise torque = clockwise torque

(force)(lever arm) = (force)(lever arm)

(force) (20) = (.98) (30)

20force = 29.4

force = 29.4/20

force = 1.47N

The question asked for the MASS of the meter stick, so we need to convert 1.47N back to mass.

w=mg

1.47 = (m)(9.8)

m = 1.47/9/8

m = 1.5kg

m=150g

The mass of the meter stick is 150g

Rotational Inertia/Angular Momentum & Center of Mass/Gravity

This video is about Rotational Inertia and Angular Momentum. I like this video for multiple reason; it makes the definitions easy to understand, teenagers created it and it has examples that we have used in class, both of which make it relatable. Rotational inertia is the amount of resistance an object has to rotate. The video related rotation inertia to mass by saying, "rotational inertia depends on where the concentration of mass is. If it is close to the axis of rotation, it will have a small inertia and if it is far away, it will have a big inertia". I thought inertia was how big the object was, but that definition really cleared it up for me. The video also made clear that rotational inertia and rotational velocity are inversely proportional to each other, which makes the conservation of angular momentum law make sense (angular momentum before=angular momentum after). I found this video very useful.


This video explains the center of mass through acceleration and numbers, so if you wanted to know exactly how to solve for the center of mass you could use this video. Although, for our purposes the center of mass and center of gravity will almost always be the same.


This video gives one specific example of the center of gravity, and it completely changed how I saw it. After you watch the experiment, you will see how all three points of the wooden board meet at one point in the middle (the center of mass).