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# Angular Kinetics Review - PowerPoint PPT Presentation

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. Torque and Motion Relationships. Relationship between linear and angular motion

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• 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

• 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

T = I

What is torque?

What is rotational inertia,

Or moment of inertia?

What is Moment of Inertia? Constant

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

What is radius of gyration (k)? Constant

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

Determining MOI & K Constant

• Simple 3-segment system:

• I = 3mi di2 = m1 d12 + m2 d22+

m3 d32 + . . . . . . .+ mi di2

• I = mk2 ; k = (I/m).5

• Irregularly shaped bodies

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

• 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

Changing ConstantIandk in the human body

Changing ConstantIand k in the human body

Angular Momentum positions

• 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 329-331)

• Angular momentum is constant if net impulse is zero