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Center of Mass

Jane Doe

Jane Doe

3 min read

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Study Guide Overview

This study guide covers the center of mass (COM) in AP Physics C: Mechanics. It defines COM as the average position of mass and the balance point. The guide explains how to calculate COM for a system of discrete masses using a weighted average formula. It also discusses linear mass density.

AP Physics C: Mechanics - Center of Mass Study Guide 🚀

Hey there, future physicist! Let's get you prepped for the AP Physics C: Mechanics exam with a deep dive into the Center of Mass. This guide is designed to be your go-to resource, especially the night before the exam. Let's make sure you're feeling confident and ready to ace it!

Center of Mass (COM) and Linear Mass Density

What is the Center of Mass? 🤔

The center of mass is the average position of all the mass in an object or system. Think of it as the balance point. If you could balance an object on a single point, that point would be the center of mass. It's where the object is perfectly balanced in a gravitational field.

Key Concept
  • It's the mean position of every section of the object or system, weighted by mass.
  • It's the balance point of an object.

Calculating the Center of Mass

For a System of Discrete Masses:

Imagine a bunch of point masses scattered around. The COM is found by averaging their positions, weighted by their masses:

Xcm=m1x1+m2x2+...+mnxnm1+m2+...+mn=i=1nmixii=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}

Question 1 of 4

The center of mass of an object or system can best be described as which of the following? 🤔

The point where the object is the most dense

The average position of all the mass in the object or system

The geometric center of the object

The point farthest from any mass