# Ch-7 - Chapter 7 Rotational Motion and The Law of Gravity...

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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 =
Radians and Degrees 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 The  angular displacement  is defined as the angle an  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 θ θ = -
Average Angular Speed The average angular  speed,  , of a rotating  ω rigid object is the ratio of  the angular displacement  to the time interval f i av f i t t t θ θ θ ϖ - = = -

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Instantaneous Angular Speed 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 (clockwise) θ
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 ϖ ϖ α - = = -

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Instantaneous Angular  Acceleration Units of angular acceleration are rad/s ² Positive angular accelerations are in the counterclockwise
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