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Rotational Motion Chapter 8

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Describing Rotational Motion 8.1

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Describing Rotational Motion Radian Angular Displacement – change in an angle

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Practice Problem What is the angular displacement in radians of a wagon that moves 135 around a circular path?

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Angular Velocity

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Practice Problem A playground merry-go-round makes two complete rotations in 9.6s. What is its angular velocity?

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Angular Acceleration

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Practice Problem A car increases in speed from rad/s to rad/s in 5.0 s. What is the angular acceleration of the car?

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Homework Page 200 – 5-9

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Rotational Dynamics 8.2

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Starting Rotation of Object lever arm – perpendicular distance from the axis of rotation to the point where the force is exerted – L= rsinθ – θ=angle at which the force is applied!!! – r=distance to point where force is applied to axis

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Torque measure of how effectively a force causes rotation – N*m – τ (tau)

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Practice Problem How much torque is applied if a wrench applies a force of 240N at an angle of 60.0° from the perpendicular? The wrench is 32cm long.

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Net Torque Net=Sum decide on a positive & a negative rotation direction τ=τ 1 +τ 2

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Practice Problem Ashok, whose mass is 43kg, sits 1.8m from the center of a seesaw. Steve, whose moss is 52 kg, wants to balance Ashok. How far from the center of the seesaw should Steve sit?

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Homework Page 203: Page 205: 17-20

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The Moment of Inertia resistance to rotation I kg*m 2 different for different shapes Point Mass – I=mr 2

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Practice Problem What is the moment of inertia of a hockey puck that has a mass of 170g, a thickness of 2.5 cm, and a diameter of 7.6 cm? The formula for the moment of inertia of a cylinder is I=1/2mr 2.

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Homework Page 208: problems 21-24

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Newtons Second Law of Rotation Replace Newtons Second Law (F=ma) with angular terms a=α F=τ net m=I

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Practice Problem A solid steel wheel has a mass of 15kg and a diameter of 0.44m. It starts at rest. You want to make it rotate at 8.0 rev/s in 15s. – What torque must be applied to the wheel? – If you apply the torque by wrapping a strap around the outside of the wheel, how much force should you exert on the strap? – If the force on the strap were twice as great, what would be the speed of rotation of the wheel after 15s?

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Equilibrium 8.3

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Center of Mass the point on the object that moves in the same way that a point particle would move Locating – Suspend the object from a point, center of mass is along the vertical line drawn – intersection of 2 vertical lines will give a point Center of mass for a person – different male & female

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Center of Mass and Stability Stable – an external force is required to tip object Higher center of gravity – less force needed to upset Equilibrium – translational equilibrium – rotational equilibrium

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Practice Problem A 5.8kg ladder, 1.80m long, rests on two sawhorses. Sawhorse A is 0.60m from one end of the ladder, and sawhorse B is 0.15m from the other end of the ladder. What force does each sawhorse exert? – What if the mass of the ladder is 11.4kg?

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Homework Page 210: Page 215: 37-39

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Rotating Frame of Reference Centrifugal Force – apparent force (not real) – pulls toward the outside of the rotation Coriolis Effect – deflection of a moving object

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Homework Page 217: Page 223: 75, 78, 81, 84, 88 MAKE SURE YOU STUDY FOR YOUR TEST TOMORROW!!! ***IF YOU HAVE QUESTIONS ASK***

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