chapter7 - Chapter7 RotationalMotion and TheLawofGravity...

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Chapter 7 Rotational Motion and The Law of Gravity
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The Radian The radian is a unit  of angular measure The radian can be  defined as the arc  length s along a  circle divided by the  radius r   s r θ=
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More About Radians Comparing degrees and radians Converting from degrees to radians ° = π ° = 3 . 57 2 360 rad 1 ] rees [deg 180 ] rad [ θ ° π = θ
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Angular Displacement Axis of rotation is  the center of the  disk Need a fixed  reference line During time t a, the  reference line  moves through  angle  θ
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Rigid Body Every point on the object undergoes circular  motion about the point O All parts of the object of the body rotate  through the same angle during the same time The object is considered to be a  rigid body This means that each part of the body is fixed in  position relative to all other parts of the body
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Angular Displacement, cont. The  angular displacement  is defined as the  angle the object rotates through during some  time interval   The unit of angular displacement is the radian Each point on the object undergoes the same  angular displacement f i θ = -
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Average Angular Speed The average  angular speed,  , of  ω a rotating rigid  object is the ratio of  the angular  displacement to the  time interval f i av f i t t t θ ϖ - = = -
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Angular Speed, cont. The  instantaneous  angular speed is defined  as the limit of the average speed as the time  interval approaches zero Units of angular speed are radians/sec rad/s Speed will be positive if   is increasing  θ (counterclockwise) Speed will be negative if   is decreasing  θ (clockwise)
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Average Angular Acceleration The average angular acceleration    of  an object is defined as the ratio of the  change in the angular speed to the time  it takes for the object to undergo the  change: α f i av f i t t t ϖ α - = = -
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Angular Acceleration, cont Units of angular acceleration are rad/s² Positive angular accelerations are in the  counterclockwise direction and negative  accelerations are in the clockwise direction When a rigid object rotates about a fixed axis,  every portion of the object has the same  angular speed and the same angular  acceleration
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Angular Acceleration, final The sign of the acceleration does not  have to be the same as the sign of the  angular speed The instantaneous angular acceleration  is defined as the limit of the average  acceleration as the time interval  approaches zero
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Analogies Between Linear and  Rotational Motion
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chapter7 - Chapter7 RotationalMotion and TheLawofGravity...

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