1. Center-of-Mass When we think about objects in motion, we automatically use that object’s Center-of- Mass in our calculations. But what is the Center-of-Mass? If we say an object has evenly distributed mass, we mean that all its mass is evenly distributed about a single point. That point is its Center-of-Mass. For a meter stick 100cm long, its center of mass would be in the middle at the 50cm point. 0 50 100 CM If an object’s mass is NOT evenly distributed, we can still find the single point where as much mass is to one side as the other. That point is its Center-of-Mass. For a wrench 100cm long, its center of mass would NOT be in the middle at the 50cm point. CM The Center-of-Mass is shifted closer to the more massive side.

2. An object’s Center-of-Mass can be shifted horizontally when its mass is not distributed evenly. An object’s Center-of-Mass can ALSO be shifted vertically when its mass is not evenly distributed. Example: A forklift’s horizontal Center-of-Mass is normally about here: CM But if there is a mass on the forks, then the Center-of-Mass is shifted forward: CM And if the forks are raised, the Center-of-Mass will rise also: A forklift’s vertical Center-of-Mass is normally about here: CM Raising the Center-of-Mass makes an object UNSTABLE !

3. How to find the Center of Mass: Consider a common brick 20cm long, 10cm high and 12 cm deep. Its mass is evenly distributed. In the x direction, all its mass is centered at 10cm (half way) In the y direction, its mass would be centered at 5cm (half way) In the z direction, its mass would be centered at 6cm (halfway) x y z 020 cm 10 cm 12cm It’s easy if the object’s mass is evenly distributed. CM x CM y CM z The Center-of-Mass is half-way in each axis. The CM is at the coordinate: (10, 5, 6)

4. How to find the Center of Mass: It’s NOT as easy if the object’s mass is unevenly distributed. We need to use an equation: CM = (m 1 *d 1 ) + (m 2 *d 2 ) + (m 3 *d 3 ) +... m 1 + m 2 + m 3 +... Each object’s mass Distance from a reference point A forklift will pick up a 1m long pallet loaded with three boxes of different masses. The boxes are centered at 0.2m, 0.5m, and 0.75m away from the left edge of the pallet. Find the Center-of-Mass. 10kg 30 kg 60 kg 0.2m 0.5m 0.75m (10kg*0.2m) + (30kg*0.5m) + (60kg*0.75m) 10kg + 30kg+ 60kg CM = CM = 0.62m from the left edge The CM is not in the middle (0.5m) because the mass is not evenly distributed. It is more toward the more massive boxes.