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  2. AP Physics C Mechanics
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How to calculate the Center of Mass for a System of Discrete Masses?

Use the formula: Xcm=m1x1+m2x2+...+mnxnm1+m2+...+mn=∑i=1nmixi∑i=1nmiX_{cm} = \frac{m_1x_1 + m_2x_2 + ... + m_nx_n}{m_1 + m_2 + ... + m_n} = \frac{\sum_{i=1}^{n} m_ix_i}{\sum_{i=1}^{n} m_i}Xcm​=m1​+m2​+...+mn​m1​x1​+m2​x2​+...+mn​xn​​=∑i=1n​mi​∑i=1n​mi​xi​​.

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How to calculate the Center of Mass for a System of Discrete Masses?

Use the formula: Xcm=m1x1+m2x2+...+mnxnm1+m2+...+mn=∑i=1nmixi∑i=1nmiX_{cm} = \frac{m_1x_1 + m_2x_2 + ... + m_nx_n}{m_1 + m_2 + ... + m_n} = \frac{\sum_{i=1}^{n} m_ix_i}{\sum_{i=1}^{n} m_i}Xcm​=m1​+m2​+...+mn​m1​x1​+m2​x2​+...+mn​xn​​=∑i=1n​mi​∑i=1n​mi​xi​​.

What is the definition of Center of Mass?

The average position of all the mass in an object or system; the balance point.

What does center of mass represent?

The mean position of every section of the object or system, weighted by mass.