1. Rotational Equilibrium & Dynamics
8-2: Equilibrium & Center of Mass

2. 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?

3. 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:
1. Translational EquilibriumSF=0—the net force on the object must be zero.
2. Rotational EquilibriumSt=0—the net torque on the object must be zero.

4. 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!!!

5. Sample Problem #1
Where must the kid on the right be sitting for the system to remain in rotational equilibrium?

6. Sample Problem #2
A 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?

7. 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 masscenter of gravity.
Emphasize the definition of center of gravity—the point at which the gravitational force acts as if the object were a point mass.

8. 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

9. Check Yourself Where is the center of gravity of a donut? XCG
(Notice the center of gravity is located outside of the object!)

10. Solving Equilibrium Problems
Draw a picture and label the appropriate forces.
Apply 1st condition for equilibrium—SF=0.
Choose an axis of rotation (be clever about it).
Apply 2nd condition for equilibrium—St=0.

11. 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?

12. Solution: Given: L=20.0 m FB= 4.00x105 N FC= 1.96x104 N Unknown: FP1

13. Stability and Toppling
An object is stable if its CG is above its base.
STABLE CG CG
UNSTABLE
Weight
Weight
Axis
BASE
BASE
Axis

14. Stability and Toppling
Example

15. Check Yourself Three trucks are parked on a slope. Which truck(s) tip
over?
BASE CG CG CG 15

16. Demo: Picking candy off the floor

17. Coca-Cola Demo: Balance the Can x CG
Ask: Why can’t I stand a pop can on edge? Is it possible? What would I have to do to make it work? x CG 17

18. Demo: Magic anti-gravity Bottle holder

19. Q: Why does a ball roll down hill?