Equilibrium: Balance & Stability

What is center of gravity?

COG is the point through which the force of gravity acts

• It is the point on a system around which its weight is evenly distributed or balanced 

Describe how where weights are placed in a system affects position of COG

If the weights are all placed on one side, the position of COG would shift towards the heavier end

The COG shifts to the heavier side because there is greater torque on that side, and the COG is always where the torques on both sides balance

Effect on COG when body leans to the side

The position of COG shifts to the side where the weight is concentrated ie. COG shifts to the side we’re leaning

The vertical position of the COG is influenced by what?

Height

As more weight is added to the top of the system, the COG shifts upwards

COG affects ability to ____/respond to _____

control; forces

Where is the COG for baby crawling ie. body towards the ground?

COG is outside of the body — it’s between the body and the ground.

For a baby, it’s easier to hold the position as the COG is lower

What 2 things influence the position of COG

The position of COG can shift. How much it shifts depends on:

1. Weights of the segments moved

2. the distance moved 

Name and motion for force acting through COG

Centric
Rectilinear motion

Name and motion for force acting off the COG

Eccentric force 

Rotation and curvilinear

Name and motion for force acting on opposite sides, off center, equidistant from COG

Couple 

Rotation 

What is equilibrium?

CONTROL

Equilibrium is a physical state in which opposite forces equal out

What is balance?

Balance is an even distribution of weight enabling the system to remain upright and steady

Balance is a static concept 

→ A system’s abillity to control equilibrium is called balance

Stability

Capacity of an object to return to equilibrium or to its original position after it has been displaced

• Stability is a dynamic concept

• It is related to responding to external forces

• Only when there’s a change taking place (responding to change)

Static vs dynamic equilibrium

Static Equilibrium:

• Static here means staying still/not moving

• Static eq = balance 

• In control and in equilibrium but not moving 

Dynamic Equilibrium: 

• Stability 

• Form of control when moving

• e.g. reflex when falling down: generating forces to undo the fall is dynamic equilibrium/stability

What is needed for an object to be in balance/state of equilibrium

For an object to be in balance/state of equilibrium, the external forces acting on it or the moments of those forces must sum to zero

• In control, not moving

• Opposing forces equal out

Static equilibrium explained thru formula

Sum of Fx (horiz) and Fy (vert) forces = 0

Sum of torque (rotational forces) = 0 

Dynamic equilibrium explained thru formula

System is accelerating but in control over any external influences

You’re moving, but the net effect of all the forces/torque that are present is equal to the mass x acceleration already occurring — so the system stays in a stable

Hence:

Sum of all forces (x and y) and torque (rotational inertia x angular acceleration) minus mass x acceleration is 0

Why is stability affected by COG?

Because COG of an object is its balance point or the sum about which the moments of force created by the weights of all the parts of the object sum to zero

Define base of support

Area bound by the outermost regions of contact between a body and support surface → area of contact

How is balance and stability related to base of support

We want to maintain our COG within the base of support

When you shrink the base of support, you shrink the room for error

• Small movements push the COG towards the edge of base of support, making you less stable

Shifting the COG to which two areas cause instability?

1. Shifting the COG to the anterior-posterior edge of the base of support 

2. Shifting the COG to the lateral edge of the base of support 

What happens to stability as the COG/COM moves up the system?

When a system’s COG is higher, any motion or force applied to it results in a larger torque around its pivot point, making it more likely to tip over. 

As COG decrease, balance ____

As COG increases, balance ____

increases, decreases

Explain the third and fourth factors that affect stability

1. Mass: more mass, more resistance to change (inertia) = more stability

2. Friction: more mass → more ground rxn force = more friction = more stability

What can you do in tug of war to increase stability?

1. Increase base of support with wider stance

2. Lower yourself to lower your COG

How does a pole help with tightrope walking?

1. As rotational resistance to change (rotational inertia) increases, stability (ability to respond to external forces) increases

2. Lowers the position of the COG to increase stability 

3. Adds/increases mass (m) and distribution of mass (k) which increases moment of inertia

Eve:

1. Increases mass

2. Increases the distribution of masses (increases radius of gyration) which increases the moment of inertia

3. Pole curves downwards which helps lower COG

What are the factors affecting a system’s stability?

1. Mass

2. friction

3. location of COG

4. base of support

Difference between static and dynamic equilibrium

Static eq = motionless state

Dynamic eq = system in motion where all acting forces result in equal and oppositely directed forces

What is a couple?

Two eccentric forces that produce rotation only