Chapter10

# Chapter10 - Chapter 10 Demos:

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PHYS276, S09 Chapter 6 1 Chapter 10 Demos: http://www.physics.umd.edu/deptinfo/facilities/lecdem/lecdem.htm B2-22: levers – torque – physical definition D2-01: ring and disc on inclined plane D1-53: loop the loop C4-21: atwood machine Plus some of chapter 11 Thanks to Prof LaPorta and “Peer Instruction” by Eric Mazur

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Introduction PHYS276, S09 Chapter 6 2 D2-01: ring and disk on inclined plane We have studied how the center-of-mass of an extended object moves. We will now study the motions of the various parts of the extended object relative to the center of mass. Especially, for a rigid object, we’ll study rotations We will also learn to understand interesting phenomena like the following.
We need some suitable variables to describe this motion PHYS276, S09 Chapter 6 3 x = r cos α y = r sin = s / R Already know: New: Δϕ angular displacement ω d ϕ dt angular speed d dt d 2 dt 2 angular acceleration Angular velocity: define a vector whose magnitude is the angular speed and direction is given by a right-hand rule. We can also use this to describe the rotation of a rigid body around a fixed axis by imagine a line on the object passing through the rotation axes sweeping out angles. What are the units for α and ω ?

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Chapter 10 Rotation Rotational quantities are vectors. Vector direction is defined by the axis of rotation. Right hand rule Curl your fingers in the direction of rotation, your thumb will point along the angular velocity vector ω
PHYS276, S09 Chapter 6 5 ω = 2 π f = 2 T

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Test yourself PHYS276, S09 Chapter 6 6 A bug sets on a turntable that is spinning in the direction shown (counter clockwize) but slowing down . What is the direction of the angular acceleration? 1) +x 2) -x 3) +y 4) -y 5) +z 6) -z 7) None of the above +z +x +y
Constant Angular Speed PHYS276, S09 Chapter 6 7 Imagine the red dot moving around the circle at constant speed, v. Then its coordinates, as a function of time, are: r = R ϕ = v t R ω = v R α = 0 Look at units likesize, = a || R

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Constant angular acceleration PHYS276, S09 Chapter 6 8 α = 0 (a constant) by integration: Δω = 0 t →ω = 0 t + ω 0 Δϕ = 1 2 0 t 2 + 0 t
Example PHYS276, S09 Chapter 6 9 What angular acceleration would be needed to get a disk with radius 0.05m at rest spinning at 10 rpm in 0.1 seconds? What would the speed of a point on the rim be at that time? f = (10 rev min )( 1min 60 s ) = 0.17 s 1 ω = 2 π f = 1 s 1 = 0 + α t 1 = 0 + (.1) = 10 s 2 (we are not told if it is spinning clockwize or counter, so we don’t know direction) Remember frequency and angular frequency are not the same thing v = r = (0.1)(0.05) = 0.005 m / s

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Rotational kinetic energy PHYS276, S09 Chapter 6 10 Two balls connected by massless rod that has a hole with a pin through it. You give it a spin so that
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Chapter10 - Chapter 10 Demos:

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