AP Physics
1
Explorer
2.1 · center of mass
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x_cm = Σmᵢxᵢ / Σmᵢ
weighted average position
heavier mass pulls CoM toward it
Mass 1
m₁ · mass
3 kg
x₁ · position
-4 m
Mass 2
m₂ · mass
1 kg
x₂ · position
4 m
x_cm
— m
total mass
— kg
Three masses (2D)
m₁ (top)
2 kg
m₂ (bottom-left)
2 kg
m₃ (bottom-right)
2 kg
x_cm
— m
y_cm
— m
total mass
— kg
Ball 1 (top)
m₁ · mass
1 kg
v₁ · velocity
1 m/s
Ball 2 (bottom)
m₂ · mass
1 kg
v₂ · velocity
1 m/s
gap · vertical spacing
80 px
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v_cm
— m/s
x_cm
— m
CoM = weighted average position
heavier mass pulls CoM toward it
CoM moves at constant v
if no external forces act
① 1D · Two Masses
x_cm on number line
② 2D · Triangle
x_cm y_cm crosshair
③ Motion · Two Balls
CoM tracks constant v
Center of Mass:
x_cm = (m₁x₁ + m₂x₂) / (m₁ + m₂). Drag masses and positions — the CoM (amber marker) is always pulled toward the heavier mass.