Lecture21

Lecture21 - PHYSICS 149: Lecture 21 Chapter 8: Torque and...

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PHYSICS 149: Lecture 21 • Chapter 8: Torque and Angular Momentum – 8.2 Torque – 8.4 Equilibrium Revisited – 8.8 Angular Momentum Lecture 21 Purdue University, Physics 149 1
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Midterm Exam 2 • Wednesday, April 6, 6:30 PM – 7:30 PM • Place: PHY 333 • Chapters 5 - 8 • The exam is closed book. • The exam is a multiple-choice test. • There will be ~15 multiple-choice problems. – Each problem is worth 10 points. • Note that total possible score for the course is 1,000 points (see the course syllabus) • The difficulty level is about the same as the level of textbook problems. • You may make a single crib sheet – you may write on both sides of an 8.5” × 11.0” sheet Lecture 20 2 Purdue University, Physics 149
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Lecture 21 Purdue University, Physics 149 3 Rotational Kinetic Energy • Consider a mass M on the end of a string being spun around in a circle with radius r and angular frequency ω – Mass has speed v = ω r – Mass has kinetic energy K = ½ M v 2 = ½ M ω 2 r 2 • Consider a disk with radius R and mass M, spinning with angular frequency ω – Each piece of disk has speed v i = ω r i – Each piece has kinetic energy K i = ½ m i v 2 = ½ m i ω 2 r i 2 – Combine all the pieces Σ K i = Σ ½ m i ω 2 r 2 = ½ ( Σ m i r i 2 ) ω 2 = ½ I ω 2 • Rotational Inertia I = Σ m i r i 2 (units kg m 2 ) M r i
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Lecture 20 Purdue University, Physics 149 4 Rotational Inertia Table For objects with finite number of masses, use I = Σ m r 2 . For continuous objects, use table below.
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Lecture 20 Purdue University, Physics 149 5 Torque • Rotational effect of force. Tells how effective force is at twisting or rotating an object. τ = ± r F perpendicular = r F sin θ τ = ± r perpendicular F r perpendicular = lever arm – Units N m – Sign, CCW rotation is positive F
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Torque • Torque measures the effectiveness of a force for twisting or turning an object. – Magnitude: – Sign: • If a torque causes a CCW rotation, assign “+” sign. • If a torque causes a CW rotation, assign “-” sign. – Direction: • If a torque causes a CCW rotation, the torque’s direction is “out of” the plane and normal to the plane. • If a torque causes a CW rotation, the torque’s direction is “into” the plane and normal to the plane. • Torque is a vector quantity. • Units: N m – But, torque is not a form of energy. • Torque is denoted by τ beyond the scope of this class lever arm Lecture 20 6 Purdue University, Physics 149
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Lecture 21 Purdue University, Physics 149 7 Torque • Rotational effect of force. Tells how effective force is at twisting or rotating an object. τ = ± r F perpendicular = r F sin θ – Units N m – Sign, CCW rotation is positive • Work done by torque – Recall W = F d cos θ – For a wheel W = F tangential d = F tangential 2 π r θ / (2 π ) ( θ in radians) = F tangential r θ = τ θ P = W/t = τ θ /t = τ ω
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Lecture 20 Purdue University, Physics 149 8 The picture below shows three different ways of using a wrench to loosen a stuck nut. Assume the applied force F is the same in each case.
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Lecture21 - PHYSICS 149: Lecture 21 Chapter 8: Torque and...

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