Center of Mass and Equilibrium

Center of Mass

• defintion

• How it applies to linear and angular motion

Conceptual point where all mass of body considered consentrated

• Point mass

For linear motion to occur = Force through CoM

For Angular motion to occur = Force not through CoM (rotation)

Difference between Center of Mass and Center of Gravity

COM = point where distribution of MASS equal

COG = point where distribution of WEIGHT equal (depending on gravity, Newtons)

Gravitational Forces

• Definition

• force of attraction between 2 masses

  • Depends on masses involved and their separation

Finding COG from the COM

• method

• knifes edge method to find equilibrium of unequal shape

• Balance it on its COM = indirectly used to estimate COG

Equilibrium of System

• what creates equilibrium (2 things)

• Explain moments

• Equation for moments

∑ forces on body = 0

∑ moments about a point = 0

• The moment of force (torque) about an axis depends on the applied force, and the distance of the force from the pivot point

• Moment (Nm) = Force (N) x Perpendicular distance (m)

Determining COG of whole body

• 2 methods and defintion

1. Statograph - device that sums the moments about an axis

2. Reaction Board - device that sums 2 axis

Determining COG for parts of a body

• method

• Limitation

• Why we have to use it nonetheless

1. Segmental Method

• Not accurate = assumptions and standard data

• Arm connected to body so can’t use reaction board or statograph