1. Angular Kinetics Review
Source: Chapter 12 of Basic Biomechanics by Susan Hall
Reference to figures in this presentation refer to the former text by Kreighbaum, which is on reserve

2. Torque and Motion Relationships
Relationship between linear and angular motion
displacement, velocity, and acceleration (Fig H.1, p 315)
Angular analogue of Newton’s third law (F=ma), the instantaneous effect of a force or torque
Torque = moment of inertia (I) X angular acc ( (Fig H.5-H.7)
What is torque?
What is moment of inertia ?(Fig H.3, p 319)
What is radius of gyration (Fig H.4, p 320)
Changing moment of inertia and radius of gyration in the body (Figures H.8 and H.9, p 323 and 324)
Calculations using a 3-segment system
Homework problem

3. Relationship between linear and angular motion (kinematics)

4. Instnataneous effect of net torque: Moment of Inertia Constant
What is torque?

5. Instantaneous effect of net torque: Torque is constant
What is rotational inertia,
Or moment of inertia?

6. Instantaneous effect of net torque: Ang acc constant

7. What is Moment of Inertia?
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

8. 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

9. 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!

10. 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

11. MOI & K – Geometric Objects

12. Changing I and k in the human body

13. Changing I and k in the human body

14. MOI around principal axes of human body in different positions

15. Angular Momentum
Impulse-momentum relationship - effect of force or torque applied over time
Linear: Ft = mv Rotational: Tt = I 
What is angular impulse? (Fig I.1, I.2, I.3, p 327-8)
Torque X time
What is angular momentum? (Fig I.4, p 329)
amount of angular movement: I 
Conservation of angular momentum (Fig I.4, I.5, I.6 p )
Angular momentum is constant if net impulse is zero

16. What is angular impulse?

17. Angular Impulse: Mediolateral axis

18. Angular Impulse around vertical axis

19. What is angular momentum (L)?

20. Conservation of Momentum

21. Conservation of Momentum