week 12 – angular kinetics objectives identify and provide examples the angular analogues of mass,...
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Week 12 – Angular Kinetics Objectives
• Identify and provide examples the angular analogues of mass, force, momentum, and impulse.
• Explain why changes in the configuration of rotating airborne body can produce changes in the body’s angular velocity (conservation of momentum principle)
• Define centripetal force and explain where and how it acts
• Solve quantitative problems relating to the factors that cause or modify angular motion
Week 12 Angular Kinetics• Read Chapter 14 of text• Reference to figures in this presentation refer to the former text by
Kreighbaum, which is on reserve• Self-study problems
– Sample problems: • #1, p 459 – angular momentum calculation• #2, p 462 – conservation of angular momentum• #3, p 466 – angular impulse and change in angular momentum calculation• #4, p 469 – Angular analogue of Newton’s law of acceleration
– Introductory problems, p 472: #5,6,7,9
• Homework problems (due Monday, November 28)– Additional problems, pp 473-474: #1,4,5– Additional handout problem on moment of inertia
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
• Sample problem #4, p 469– 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
Instantaneous effect of net torque: Torque is constant
What is rotational inertia, Or moment of inertia?
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
Angular Momentum• What is angular momentum? (Fig I.4, p 329)
– amount of angular movement: I – Sample problem #1, p 459
• 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– Sample problem #3, p 466
• Conservation of angular momentum (Fig I.4, I.5, I.6 p 329-331)– Angular momentum is constant if net impulse is zero– Sample problem #2, p 462