1. Biomechanical Considerations for Striking Implements - Background
Relationship between linear motion and rotary motion
Radius of rotation
Axis of rotation
Relationship between torque and rotational motion
Moment of Inertia: I = mk2
Radius of gyration: k = (I/m).5
Rotational analogues of newton’s laws: T = I
Elastic properties of striking implements
Coefficient of restitution
Vibrations during the swing (bending)
Vibrations during and after impact
Sweet spot determinants
Center of percussion, vibrational nodes

2. Relationship between linear and angular motion (kinematics)

3. Relationship between linear and angular motion
Would you rather have a long or short baseball bat or tennis racquet? Why?

4. What is Moment of Inertia (MOI)?
It is the resistance of a system to rotational acceleration, and is
calculated at follows:
Here, r (the radius of rotation) is equal to k (the radius
of gyration), but that is not the case with extended bodies

5. What is radius of gyration (k)?35
An indicator of distribution of mass
about the axis. It is the distance from
the axis to a point at which all the
mass of a system of equal mass
would be concentrated to have the
MOI equal the original system. It
is, then, the average weighted
distance of the mass of a system
to the axis.
Equivalent systems k 35

6. Determining MOI & K Irregularly shaped bodies Simple 3-segment system:
I = 3mi di2 = m1 d12 + m2 d22+
m3 d mi di2
I = mk2 ; k = (I/m).5
Irregularly shaped bodies
But we can’t measure all of these small masses!

7. Physical pendulum properties (rigid bodies)
Radius and axis of rotation
Radius of gyration (K)
Moment of inertia (MOI)
Center of percussion

8. Physical pendulum method of determining MOI and K
Suspend object at axis
Measure mass (m), and distance from axis to COM, r
Measure period of oscillation (T)
Moment of inertia (I) = T2 mr * m/sec
Radius of gyration (K) = ( I/m).5

9. Rigid Body -Bat Distance from Axis to COP:
q = k2/r = I/mr = T2g/42 = T2

10. Rigid Body - Tennis Racket

11. Rigid Body - Golf Club

12. Semi-rigid (elastic) bodies)
Coefficient of restitution
Vibrations - nodes and modes
Vibrations when bat is free
(during impact with ball)
Vibrations when bat is clamped
(during swing )

13. Simpler illustration of bat vibrations during swing and impact
Approx Hz
Approx HZ

14. Bat Vibrations During Swing and Impact

15. Coefficient of Restitution (COR)
COR is a measure of liveliness of an object and increases directly with temperature and inversely with impact velocity.
COR of balls dropped
or thrown at a rigid
wooden surface is
Shown here

16. Questions What is the sweet spot of a striking implement?
How do we take advantage of rigid body properties to improve implement?
How do we take advantage of elastic properties to improve implement?

17. Evaluation methods for striking implements
Apply scientific principles to evaluate mfgr claims
Use it yourself, if possible
Product reviews on the internet & in trade mags
Consult with others who use it, or supervise its use
Consult with professors, or professionals (e.g., coaches) with specialized insight and expertise
Look at research available, if any
Evaluate quality of research –
Extrinsic - who is sponsoring the research, where did it appear?
Intrinsic – methods, procedures, statistics, conclusions

18. Next: Bats & Clubs Tuesday, November 2 Thursday, November 4
Softball and baseball bats (ch 10 of text)
PPT Pres on Mechanical Properties of Bats on course website
Submit 2 questions relating to readings on bats
Thursday, November 4
Review new bat products
2004 catalogues from leading bat manufacturers
Bats from lab
Read Chapter 9 and ppt presentation on golf clubs on course website
Submit 2 questions on golf clubs