Angular Kinetics Review

• Readings: Hamill Ch 11

• Sources for PPt presentation:

• Chapter 12 of Basic Biomechanics by Susan Hall and Kreighbaum’s text

• Reference to figures in this presentation refer to the former text by Kreighbaum, which is on reserve

Torque and Motion Relationships• Relationship between linear and angular motion

– displacement, velocity, and acceleration

• 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 (

What is torque? • What is moment of inertia ? • What is radius of gyration • Changing moment of inertia and radius of gyration in the body

Calculations using a 3-segment system• Homework problem

Relationship between linear and angular motion (kinematics)

a = r

Instnataneous effect of net torque: Moment of Inertia Constant

What is torque?

T = I

Instantaneous effect of net torque: Torque is constant

What is rotational inertia, Or moment of inertia?

Instantaneous effect of net torque: Ang acc constant

What is Moment of Inertia?

Here, r (the radius of rotation) is equal to k (the radius of gyration), but that is not the case with extended bodies

It is the resistance of a system to rotational acceleration, and is calculated at follows:

What is radius of gyration (k)?

An indicator of distribution of massabout the axis. It is the distance fromthe axis to a point at which all themass of a system of equal masswould be concentrated to have the MOI equal the original system. Itis, then, the average weighted distance of the mass of a systemto the axis.

Equivalent systems

k 35

k 35

Determining MOI & K • Simple 3-segment system:

– I = mi di2 = m1 d1

2 + m2 d22+

m3 d32 + . . . . . . .+ mi di

2

– I = mk2 ; k = (I/m).5

• Irregularly shaped bodies

But we can’t measure all of these small masses!

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 * .248387 m/sec

– Radius of gyration (K) = ( I/m).5

MOI & K – Geometric Objects

Changing I and k in the human

body

Changing I and k in the human body

MOI around principal axes of human body in different positions

Angular Momentum

• Impulse-momentum relationship - effect of force or torque applied over time– Linear: Ft = mv Rotational: Tt = I

• What is angular impulse? • Torque X time• What is angular momentum?

• Amount of angular movement: I • Conservation of angular momentum • Angular momentum is constant if net impulse is zero

What is angular impulse?

Angular Impulse:

Mediolateral axis

Angular Impulse around vertical axis

What is angular momentum (L)?

Conservation of Momentum

Conservation of Momentum

COM Questions• What is COM (or COG) and why is it important?• How is COM location different for infants and how does

this affect their movement?• Is COM location different for men vs women?• How is COM different if you lose an arm and how does

this affect movement?• How does COM relate to stability? • Why do you lean to one side when carrying a load with

one arm?• Can Vince Carter, or any athlete really hang in the air?

COM/COG Concept and Calculation Method (Adrian pp 33-41)

• Concept of balancing segmental torques

• Segmental Calculation of COM – General calculation method– Information needed

• Proportionate mass of each segment

• location of COM of each segment

Segmental concept of center of mass

Segmental concept of center of mass