SHOW WORK WHERE SPACE IS GIVEN

EXPERIMENTAL

1. Mass of bat, m:   ________(kg) (it should be 0.84 kg, unless a different bat is used)
    
2. Distance from origin to center of rotation, COR:  ________(m)
    
3. Length of bat, L_bat:  ________(m)
    
4. Distance from origin to center of gravity, CG:  ________(m)
    
5. Length of string 1, L₁ (if applicable):  ________(m)
    
6. Length of string 2, L₂ (if applicable):  ________(m)
    
7. Distance from pivot point to CG, L_CG:  ________(m)
    
8. Distance from pivot point to center of rotation, L_COR:  ________(m)
    
9. Natural frequency of swinging bat in Hz, f_o:  ________(Hz)
    
10. Natural frequency of swinging bat in rad/sec, Ω_o:  ________(rad/sec)
     
11. Moment of inertia about the pendulum's pivot point, I_o:
    
    
    I_o=__________(kg*m²)
     
12. Moment of inertia about the bat's center of gravity, I_CG.
    
    
    I_CG=__________(kg*m²)
     
13. Moment of inertia about the bat's center of rotation, I_COR.
    
    
    I_COR=__________(kg*m²)
     
14. Radius of gyration, k.
    
    
    k=__________(m)
     
15. Distance from the CG to the center of percussion, l_p.
    
    
    l_p=_________(m)
     
16. Distance from the handle to the sweet spot.
    
    
    sweet spot=_________(m)

THEORETICAL

Draw a model of the bat, TO SCALE, using AT LEAST 3 simple geometrical volumes.  Label:
- names of volumes (e.g., cylinder, conical frustum) with labels (e.g., "A", "B", etc)
- draw "negative" volumes as dotted lines
- dimensions of shapes (e.g., lengths, widths, radii)
- put a "+" at each center of gravity for individual shapes (use table to determine CGs)
- distances to each CG from origin
 

1. Distance from origin to center of gravity, CG.
   
   
   
   
   
   CG:  ________(m)
    
2. Label the CG (of the whole bat) on your model with a star.
   
    
3. In the table below, list the moments of inertia for each volume in your model
    

   VOLUME LABELS	Moment of Inertia, IGG	Mass, m	Distance from Origin, d	Moment of Inertia about Origin (IGG + md2)



4. Moment of inertia about the bat's origin, I_ZZ.
   
   
   I_ZZ=__________(kg*m²)
    
5. Moment of inertia about the bat's center of gravity, I_CG.
   
   
   I_CG=__________(kg*m²)
    
6. Moment of inertia about the bat's center of rotation, I_COR.
   
   
   I_COR=__________(kg*m²)
    
7. Radius of gyration, k.
   
   
   k=__________(m)
    
8. Distance from the CG to the center of percussion, l_p.
   
   
   l_p=_________(m)
    
9. Distance from the handle to the sweet spot.
   
   
   sweet spot=_________(m)

THE "REAL SWEET SPOT"

1. Distance from the handle to the sweet spot.
   
   
   sweet spot=_________(m)
    
2. Error of experimental sweet spot:  _________(%)
    
3. Error of theoretical sweet spot:  _________(%)