Hey, let's just move this really heavy object over here. It should be easy, right? Well, I guess things didn't go as well as they would have liked.

Why did this crane tip over as it turned but not at the beginning? One way to look at this problem is by looking at the center of gravity (on Earth this is essentially the same as the center of mass).

## What is the center of gravity?

Suppose I have some rigid object made of 4 very tiny masses that are connected by zero mass sticks. Yes, this sounds crazy but this is what we do to derive things. We start with things that seem impossible but in the end it will work for many other cases (see spherical cow).

Here are my four tiny masses. They have different masses, just for fun.

Now suppose I push up on this rigid object at the location of mass 4. In this case, there is a gravitational force on each of the 4 masses along with the force pushing up.

When dealing with rigid objects, there are really two things that we are interested in - what is the net force and and what is the net torque? First, for the forces. Clearly, there are only forces in the vertical direction (I will call this the *y* direction.)

In case you can't tell, I am using *M* to represent the sum of the 4 masses. What we get from this equation is an expression for the acceleration. Maybe the rigid object will fall or maybe it won't - but there will be some value for the vertical acceleration.

Now, what about torque? Clearly, this rigid object could change its rotational motion. I can calculate the torque about an axis that runs through mass 4. For, this case, I can use the simplified calculation of torque as: