Physics Worksheet

⚖️ Center of Mass

Chapter: Mechanics · Level ★★☆ · Time: 30 min

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After this worksheet you can

Understand: Center of Mass DefinitionUnderstand: Center of Mass Formula (Discrete System)Understand: Center of Mass of Symmetric ObjectsUnderstand: Motion of the Center of Mass

🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4

1Two masses: 5 kg at x=0, 5 kg at x=10. Find center of mass.

2Two masses: 2 kg at x=1, 6 kg at x=5. Find center of mass.

3Three masses: 1 kg at x=0, 2 kg at x=2, 1 kg at x=6. Find center of mass.

4Why is the center of mass of a symmetric uniform object located at its geometric center?

🧮 Section B · Problem Solving ● INTERMEDIATE 4 × 3 = 12

5A wide-based object (like a pyramid) versus a narrow-based object (like a pencil standing on end) -- which is more stable and why?

6Two masses: 4 kg at x=-2, 4 kg at x=2. Find center of mass.

7Why might engineers design race cars with a very low center of mass?

8A gymnast performs a flip. Does the path of their center of mass follow a smooth parabola even while their body twists and bends?

🚀 Section C · Challenge ● CHALLENGE 2 × 2 = 4

9Two masses: 10 kg at x=0, 2 kg at x=12. Find center of mass.

10Why do objects tip over once their center of mass moves outside their base of support?

💭 Reflection — the most useful thing I learned:

A ___/4 B ___/12 C ___/4 Total ___/20 Teacher's Signature Parent's Signature

✂ answer key — fold or cut before handing out

1 = x_cm=(0+50)/10=5 2 = x_cm=(2+30)/8=4 3 = x_cm=(0+4+6)/4=2.5 4 = The mass is evenly distributed around that point in every direction, so the weighted average position is exactly the center | 5 = The wide-based object, because its base of support is larger, making it harder for the center of mass to shift outside that base 6 = x_cm=(-8+8)/8=0 7 = A lower center of mass improves stability and reduces the risk of tipping during sharp turns 8 = Yes, the center of mass follows a smooth projectile path regardless of the body's internal motion, since only gravity (an external force) acts on the overall system | 9 = x_cm=(0+24)/12=2 10 = The force of gravity acting through the center of mass creates an unbalanced torque around the edge of the base, causing rotation (tipping)