Ch 08 Rotational Kinematics

Ch 08 Rotational Kinematics - Chapter 8 Rotational...

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Chapter 8 Rotational Kinematics
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8.1 Rotational Motion and Angular Displacement In the simplest kind of rotation, points on a rigid object move on circular paths around an axis of rotation. ¾ When an object rotates, points on the object move on circular paths. ¾ The centers of the circles form a line that is the axis of rotation.
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8.1 Rotational Motion and Angular Displacement The angle through which the object rotates is called the angular displacement . o θ = Δ
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8.1 Rotational Motion and Angular Displacement DEFINITION OF ANGULAR DISPLACEMENT When a rigid body rotates about a fixed axis, the angular displacement is the angle swept out by a line passing through any point on the body and intersecting the axis of rotation perpendicularly. By convention, the angular displacement is positive if it is counterclockwise and negative if it is clockwise . Units of Angular Displacement: ± Degree: There are 360 o in a circle. ± Revolution (rev): One rev represents one complete turn of 360 o . ± Radian (rad): The most useful SI unit. SI Unit of Angular Displacement: radian (rad)
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8.1 Rotational Motion and Angular Displacement r s = = Radius length Arc radians) (in θ For a full revolution: o 360 rad 2 = π rad 2 2 = = r r 360 15 7 . 3 2 o o rad == Therefore, the radian is treated as a unitless number
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8.1 Rotational Motion and Angular Displacement Example 1 Adjacent Synchronous Satellites Synchronous satellites are put into an orbit whose radius is 4.23×10 7 m. If the angular separation of the two satellites Is 2.00 degrees, find the arc length that separates them. rad 0349 . 0 deg 360 rad 2 deg 00 . 2 = π ( )( ) miles) (920 m 10 48 . 1 rad 0349 . 0 m 10 23 . 4 6 7 × = × = = θ r s r s = = Radius length Arc radians) (in θ
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8.1 Rotational Motion and Angular Displacement Conceptual Example 2 A Total Eclipse of the Sun The diameter of the sun is about 400 times greater than that of the moon. By coincidence, the sun is also about 400 times farther from the earth than is the moon. For an observer on the earth, compare the angle subtended by the moon to the angle subtended by the sun and explain why this result leads to a total solar eclipse.
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8.1 Rotational Motion and Angular Displacement r s = = Radius length Arc radians) (in θ
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8.2 Angular Velocity and Angular Acceleration o θ = Δ How do we describe the rate at which the angular displacement is changing?
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8.2 Angular Velocity and Angular Acceleration AVERAGE ANGULAR VELOCITY time Elapsed nt displaceme Angular locity angular ve Average = t t t o o Δ Δ = = θ ω SI Unit of Angular Velocity : radian per second (rad/s) Other units are : rev/min or rpm … Sign Convention: + if Δθ is + and if Δθ is
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8.2 Angular Velocity and Angular Acceleration Example 3 Gymnast on a High Bar A gymnast on a high bar swings through two revolutions in a time of 1.90 s.
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This note was uploaded on 12/03/2010 for the course PHY phy135 taught by Professor Weighgabriel during the Fall '10 term at University of Toronto.

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Ch 08 Rotational Kinematics - Chapter 8 Rotational...

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