p111_lecture16

p111_lecture16 - Chapter 8 Rotational Kinematics 8.3 The...

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Chapter 8 Rotational Kinematics
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8.3 The Equations of Rotational Kinematics
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8.4 Angular Variables and Tangential Variables velocity l tangentia = T v r speed l tangentia = T v The relationship between the (tangential) arc length, s , at some radius, r , and the angular displacement, θ , has been shown to be s = r ( in radians) Let’s find other relationships between the angular and tangential variables. Consider skaters “cracking-the-whip” :
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8.4 Angular Variables and Tangential Variables ! " # $ % & = = = t r t r t s v T ' t ! " = rad/s) in ( r v T =
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8.4 Angular Variables and Tangential Variables ( ) ( ) t r t r r t v v a o o To T T ! " = " = " = t o " # = ) rad/s in ( 2 r a T = The tangential acceleration, a T , is the change of the tangential velocity per time:
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8.4 Angular Variables and Tangential Variables Example 6 A Helicopter Blade A helicopter blade has an angular speed of 6.50 rev/s and an angular acceleration of 1.30 rev/s 2 . For point 1 on the blade, find the magnitude of (a) the tangential speed and (b) the tangential acceleration.
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8.4 Angular Variables and Tangential Variables s rad 8 . 40 rev 1 rad 2 s rev 50 . 6 = ! " # $ % & ! " # $ % & = ' ( ( ) ( ) s m 122 s rad 8 . 40 m 3.00 = = = ! r v T r ω
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8.4 Angular Variables and Tangential Variables ( ) ( ) 2 2 s m 5 . 24 s rad 17 . 8 m 3.00 = = = ! r a T 2 2 s rad 17 . 8 rev 1 rad 2 s rev 30 . 1 = ! " # $ % & ! " # $ % & = ' (
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8.5 Centripetal Acceleration and Tangential Acceleration ( ) rad/s) in ( 2 2 2 ! r r r r v a T c = = = In uniform circular motion, the only acceleration present is the centripetal acceleration.
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p111_lecture16 - Chapter 8 Rotational Kinematics 8.3 The...

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