1. Center of Gravity Pages 129 - 143
The earth pulls down on each particle of an object with a gravitational force that we call weight. Although individual particles throughout an object all contribute to weight in this way, the net effect is as if the total weight of the object were concentrated in a single point - the object's center of gravity.
5/16/2019
Dr. Sasho MacKenzie HK 376

2. Why is Jordan reaching down with his left hand?
5/16/2019
Dr. Sasho MacKenzie HK 376

3. Working Definitions Balance point of the body.
Point about which the body rotates while free in the air.
Point of the body where we can consider all of the weight of the body to act.
Near the surface of the earth, the force of gravity is the same on all parts of the body. This means that the center of gravity and center of mass of an object are the same location.
5/16/2019
Dr. Sasho MacKenzie HK 376

4. CM: Simple Example in 2D (7-iron)
There are only two parts
Shaft + Grip
Clubhead
Butt of the grip is the origin (0 cm, 0 cm)
Lets make some assumptions X Y

5. Where is the CM of the 7-iron?X Y
Grip + Shaft
Xshaft = 33 cm
Yshaft = 0 cm
Mshaft = 156 g
Clubhead
Xhead = 94 cm
Yhead = 4 cm
Mhead = 260 g S
Xshaft*Mshaft + Xhead*Mhead
Mshaft + Mhead
XCM =
Yshaft*Mshaft + Yhead*Mhead
Mshaft + Mhead
YCM =

6. Where is the CM of the 7-iron?X Y
Grip + Shaft
Xshaft = 33 cm
Yshaft = 0 cm
Mshaft = 156 g
Clubhead
Xhead = 94 cm
Yhead = 4 cm
Mhead = 260 g S
33* *260
cm =
0* *260
2.5 cm =

7. Formal/Mathematical Definition
i represents a particular particle in the body
N represents the number of particles
m is the mass of the particle
g = 9.81 m/s2
r is the moment arm distance from the CG to the particle
The equation for center of mass is conceptually the same. The difference is the lack of g.
5/16/2019
Dr. Sasho MacKenzie HK 376

8. Example: A uniform stick
Center of gravity
There are numerous particles in the stick that each have a mass. Gravity acts on all of these masses producing forces which act at a distance from the center of gravity. Because these forces act at a distance, they produce a torque. The point where all these torques balance out is the center of gravity.
5/16/2019
Dr. Sasho MacKenzie HK 376

9. Center of Mass and Torque
A common working definition for the CG is:
The balance point of an object.
The point where we can place a single finger and keep the object from rotating.
A net torque produces rotation
Therefore, the CG is the point about which the gravitational forces produce no net torque.

10. Center of Mass and Torque
Torque = Force x Moment Arm
Moment Arm: Perpendicular distance from the force to the point of rotation cm
22.875 cm
The CoG is not the point that equally divides the weight on either side of an object.
156 g
Torque:
5947.5
Torque:
5947.5
260 g

11. The center of gravity is not the point that equally divides the weight on either side of a body or object. Consider the extreme example of a sledge hammer?
C of G
There is much more weight to the right, but the moment arm is also much smaller on the right, therefore the torques will balance out.
This is why you can safely remove weights from the bar on a squat rack.
5/16/2019
Dr. Sasho MacKenzie HK 376

12. cg 1 2 cg 1 2 cg cg
Center of gravity moves in the direction the arm moved; up and to the man’s left.
Center of gravity moves in the opposite direction of the removed leg; up and to the man’s left.
5/16/2019
Dr. Sasho MacKenzie HK 376

13. 1 2 3
CG HEIGHT
GROUND
5/16/2019
Dr. Sasho MacKenzie HK 376

14. The previous slide shows three jumps with identical take-off velocities. That means that the CofG of the jumps will all reach the same height off the floor. However, by altering body position at the top of the jump, the CofG changes it’s position relative to the body, and reach height is also altered.
The following slide shows that while in the air, the CofG has a set parabolic path determined by the take-off velocity. The athlete can do nothing to change the position of his CofG while in the air. Any muscular activity will only result in relative movement about the CofG.
The illusion of hang time can be achieved by raising the limbs on the way up to peak height, and then dropping the limbs after peak vertical height is achieved.
5/16/2019
Dr. Sasho MacKenzie HK 376

15. cg 2 cg 3 cg 1
An individual watching this jump would usually focus on the position of the dancer’s head. Even though the CofG has dropped a considerable amount from 2 to 3, the head has remained at the same vertical height, thus providing the illusion of “hang time”.
This is also the case in a well executed jump shot or dunk.
5/16/2019
Dr. Sasho MacKenzie HK 376

16. 5/16/2019
Dr. Sasho MacKenzie HK 376

17. 5/16/2019
Dr. Sasho MacKenzie HK 376

18. 5/16/2019
Dr. Sasho MacKenzie HK 376

19. 5/16/2019
Dr. Sasho MacKenzie HK 376

20. 5/16/2019
Dr. Sasho MacKenzie HK 376

21. Balance
If your CofG lies within your base of support, you have the potential for balance (equilibrium)
Base of Support
Manypoint = 0
Equilibrium
Fx1 mg mg
The CofG has passed outside the base of the support and equilibrium has been lost.
Fy1
Fy2
Fy2
5/16/2019
Dr. Sasho MacKenzie HK 376

22. Factors Influencing Stability
Headstand Example
Beginners move their head out from their hands increasing their base of support, and thus their stability. However, this moves their CofG out from their hands also. When a handstand is attempted their base of support shrinks once the head leaves the floor. This now places their CofG outside of the new base of support and falling is likely.
head
CofG
CofG
Factors Influencing Stability
Weight of the body
Size of the base of support
Height of the CofG of the base of support
5/16/2019
Dr. Sasho MacKenzie HK 376