Center of MassBasic Concept

Calculating

Demos

Center of Mass:Point at which mass seems to be concentratedBalance PointRotation about

Center of Mass:Point at which mass seems to be concentratedBalance PointRotation about

Center of Mass:Point at which mass seems to be concentratedBalance PointRotation about

Finding the COM:Regular solids:

COM is the center. Show how to find X

Balances on COM:Trial and error

meter stickirregular solid

Sliding fingersmeter stickmeter stick with massbroompointerpointer on spinner

Murray’s TheoremRectangular solid

Hangs with COM below point of suspension:Chalk line/SolidsCOM isn’t in object!/High jumpers

Finding the COM:Teeter Totter equation (derive)

L

X

x m2L

m1 m2

m1 m2

Finding the COM:Teeter Totter equation in general: (weighted average!)

xCOM m1x1 m2x2 m3x3

m1 m2 m3

m1 m2 m3

X1

X2

X3

Example: Find the distance the COM is from the left side of the beam. The 45.0 kg uniform beam is 14.0 m long, has a 12.0 kg box 4.0 m from the left side, and a 30.0 kg box centered 30.0 m from the left side.

xCOM m1x1 m2x2 m3x3

m1 m2 m3

45.0 kg

12.0 kg 30.0 kg

4.0 m

7.0 m

13.0 m

8.66 m from the left side

Whiteboards: Center of mass1 | 2 | 3 | 4 | 5

TOC

The center of the 5.00 kg is 34.0 cm from the center of the 2.00 kg. How far from the 5.00 kg center is the COM? (hint: X5kg = 0)

solution

9.71 cm

5 kg 2 kg

34.0 cm

How far is the COM of the earth moon system from the center of the earth?

Earth’s mass: 5.97x1024 kgMoon’s Mass: 7.36x1022 kgEarth-Moon Distance: 3.84x108 m

(The earth’s radius is 6.38x106 m. Is this COM closer to the center or the surface of the earth?)

solution

4.68x106 m

A uniform meter stick has a mass of 85.0 grams, and I place a 15.0 gram clamp at the 24.0 cm mark, and the 55.0 cm mark. At what mark would it balance? (Assume the meter stick to have a COM at 50.0 cm)

solution

47.3 cm

A uniform meter stick has a mass of 116 grams, and has a 24.0 g mass at the 40.0 cm mark. Where do you clamp a 32.0 g mass to make it balance at the 42.0 cm mark?

solution

14.5 cm

A uniform meter stick has a mass of 95.0 grams, and has a 12.0 g mass at the 13.0 cm mark. What mass do you put at the 85.0 cm mark to make it balance at the 56.0 cm mark?

solution

37.4 g

A 75.0 kg window cleaner is 1.5 m from the right side of a scaffold that is a 62.0 kg uniform beam, 10.0 m long. There is an 18.0 kg toolbox 3.00 m from the left side. Where is the center of mass of the whole thing?

62.0 kg

18.0 kg

6.46 m from the left side, 3.54 m from the right

COM Demos!!!!!!!Irregular solids

Air Table/spin

StabilityTip O’ Meter

Miata Vs. 4Runner“g” force

Tower of pisaParadox rollerHammer and RulerFork, Spoon, matchMeter sticks: (4.0, 4.6, 5.3, 6.1, 7.3, 9.0, 11.5, 15.7, 24.0, 49.0)

HallwayKneeling/Pencil a you-cubit from your knees/hands behind back/nose to pencilToes/Nose against wall/stand on toesButt against wall, pick up pencil without bending kneesTwo footlengths from wall/Head against wall/Pick up chair/Pause/Then stand up