# Objectives

When you have completed chapter 10, you should be able to:

1. ... define "center of gravity of an object".

2. ... define "center of mass of an object"

3. ... discuss the similarities and differences between the center of gravity and center of mass.

4. ... compare the motions of the center of gravity of a projectile to the motion of some other point on the projectile.

5. ... find the center of gravity of an object at least 2 different ways.

6. ... describe the conditions necessary for an object to topple.

7. ... predict whether an object will topple, knowing the location of its center of gravity and its area of support.

8. ... distinguish among stable equilibrium, unstable equilibrium, and neutral equilibrium, and discuss the conditions for each.

10. ... give examples of how a human adjusts her center of gravity in different situations.

# Review

• Newton’s First Law – Objects move in straight lines

• Projectile Motion – Parabolic paths

#### Why should I want to know this?

The arbitrary motion of a rigid body can always be separated into a translational motion of the CM of the body, and a rotation about an axis through the CM of the body.  This greatly simplifies the analysis of the motion of the body.

# Center of Gravity/Mass

## CM and CG are Equivalent in most cases

It's good idea to just use CM rather than CG, but you will see both used interchangably.

### Exceptions

• Zero Gravity

• No CG but still has CM

• Large objects where there is a significant difference in gravity from one side to another.

Like moon, CG is closer to Earth than CM because greater effect of Earth gravity on side nearest Earth

#### Not Geometric Center for Non-homogeneous or composite objects

Variable densities or mass distributions

#### Examples of changing CG

A dangerous condition occurs when cargo or passengers move suddenly within a moving vehicle. If all of the passengers in an airliner ran to one side of the plane, it could be a problem.

Shifting cargo often causes rollovers in freight trucks by shifting the CG of the trailer/load combination.

Race cars handling changes as they burn off fuel. This changes the CG and can either improve or worsen a cars handling

## Equilibrium

Bodies always seeks position of lowest potential energy

Equilibrium State defined by motion of CG when object displaced

SEGWAY

SUMO - AKEBONE