Chapter 10 Center of Gravity/Mass



 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.


  • 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.


  • 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


Most machines, vehicles, tools, weapons


Boat, car, Axe, hammer, spear

Can/Does it change?

  • Yes for many objects
Non-rigid bodies, possibly. – like animals, body position dictates, some animals use tails for balance
  • not for Rigid bodies, no.  – it’s fixed

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

CG of common items

  • Ball bat  - near sweet spot
  • People -  in middle of body slightly below navel
  • Solar System – moves depending on position/alignment of planets
  • Basketball, Goodyear Blimp – in middle where there’s only air or helium
  • Airplanes – usually near wing level
  • Ships – below water line
  • Race cars – below axles
  • SUV’s – above axles
  • Motorcycles – between ankles

Methods of determining

  • Hang from one point, draw vertical line. Hang from a different point, draw vertical line. Intersection of lines is CM

  • Balance on fulcrum (fingers)

  • Geometric Primitives  or Calculus

  • CAD System

Motion of CG

  • Straight lines – Follows Newton’s First Law


  • Parabolic Trajectories – Review ‘Projectile Motion’




Bodies always seeks position of lowest potential energy

Equilibrium State defined by motion of CG when object displaced


  • CG rises with displacement



  • CG lowers with displacement


  • No change in height of CG (can move laterally)


  • Objects topple when CG is not above Support Area






Copyright © 2005 -  S. B. EglI