Rotational Equilibrium & Dynamics

8-2: Equilibrium & Center of Mass

Question

There is a point on a broom (or any extended object) at which it will balance perfectly. If you cut the broom at that point and weigh each part of the broom, what would you find?

Equilibrium

The ‘broom’ problem is an example of a system (object) in equilibrium

Conditions for Equilibrium:– For a system (object) to be in equilibrium it must

have: Translational EquilibriumF=0—the net

force on the object must be zero.2. Rotational Equilibrium=0—the net torque on the object must be zero.

Analysis of the broom problem

What forces are acting on the broom? What torques are acting on the broom? Which side weighs more?

Physics Rocks!!!

Sample Problem #1

Where must the kid on the right be sitting for the system to remain in rotational equilibrium?

Sample Problem #2

A 400.0 N child and a 300 N child sit on either end of a 2.0 m long seesaw. Where along the seesaw should the pivot be placed to ensure rotational equilibrium?

Center of Mass/Gravity

The center of mass is the point at which all the mass of an object can be considered to be concentrated.

The center of gravity is the point at which the gravitational force acts on an object as if it were a point mass.

In this class center of masscenter of gravity.

Position of Center of Mass/Gravity

For regularly shaped objects (sphere, cube, rod etc.), the center of gravity is located at the geometric center of the object.

XCG XCG XCG

Check Yourself

Where is the center of gravity of a donut?

XCG

(Notice the center of gravity is located outside of the object!)

Solving Equilibrium Problems

1. Draw a picture and label the appropriate forces.

2. Apply 1st condition for equilibrium—F=0.

3. Choose an axis of rotation (be clever about it).

4. Apply 2nd condition for equilibrium—=0.

Sample Problem #3

A uniform bridge 20.0 m long and weighing 4.00x105

N is supported by two pillars located 3.00 m from each end. If a 1.96x104 N car is parked 8.00 m from one end of the bridge, how much force does each pillar exert?

Solution:

Given:– L=20.0 m– FB= 4.00x105 N

– FC= 1.96x104 N Unknown:

– FP1

– FP2

Stability and Toppling

An object is stable if its CG is above its base.

CG CG

Wei

ght

BASEAxis

AxisBASE

STABLE

UNSTABLE

Wei

ght

Stability and Toppling

Example

Check Yourself

Three trucks

are parked on

a slope. Which

truck(s) tip

over?CG

CG

CG

BASEBASE

Demo: Picking candy off the floor

Demo: Balance the Can

x CGCoca-Cola

Demo: Magic anti-gravity Bottle holder

Q: Why does a ball roll down hill?