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Unformatted text preview: Chapter 7 Rotational Motion Universal Law of Gravitation Kepler’s Laws Angular Displacement • Circular motion about AXIS • Three measures of angles: 1. Degrees 2. Revolutions (1 rev. = 360 deg.) 3. Radians (2 ! rad.s = 360 deg.) Angular Displacement, cont. • Change in distance of a point: s = 2 ! r N (N counts revolutions) = r " ( " is in radians) Example 7.1 An automobile wheel has a radius of 42 cm. If a car drives 10 km, through what angle has the wheel rotated? a) In revolutions b) In radians c) In degrees a) N = 3789 b) " = 2.38x10 4 radians c) " = 1.36x10 6 degrees Angular Speed • Can be given in • Revolutions/s • Radians/s > Called # • Linear Speed at r ! = " f # " i t inradians v = 2 ! r " N revolutions t = 2 ! r 2 ! " # f $ # i (in rad.s) t v = ! r Example 7.2 A race car engine can turn at a maximum rate of 12,000 rpm. (revolutions per minute). a) What is the angular velocity in radians per second. b) If helipcopter blades were attached to the crankshaft while it turns with this angular velocity, what is the maximum radius of a blade such that the speed of the blade tips stays below the speed of sound. DATA: The speed of sound is 343 m/s a) 1256 rad/s b) 27 cm Angular Acceleration • Denoted by $ • # must be in radians per sec. • Units are rad/s ! • Every point on rigid object has same # and $ ! = " f # " i t Rotational/Linear Equivalence: ! " # ! x $ # v $ f # v f % # a t # t Linear and Rotational Motion Analogies Rotational Motion Linear Motion ! " = # + # f ( ) 2 t ! " = # t + 1 2 $ t 2 ! f = ! + " t ! f 2 2 = ! 2 2 + " # $ ! " = # f t $ 1 2 % t 2 ! x = v + v f ( ) 2 t v f = v + at ! x = v t + 1 2 at 2 ! x = v f t " 1 2 at 2 v f 2 2 = v 2 2 + a ! x Example 7.3 A pottery wheel is accelerated uniformly from rest to a rate of 10 rpm in 30 seconds. a.) What was the angular acceleration? (in rad/s 2 ) b.) How many revolutions did the wheel undergo during that time? a) 0.0349 rad/s 2 b) 2.50 revolutions Linear movement of a rotating point • Distance • Speed • Acceleration Only works for angles in radians! Different points have different linear speeds! x = r ¡ ¢ v = r ! a = R ! Example 7.4 A coin of radius 1.5 cm is initially rolling with a rotational speed of 3.0 radians per second, and comes to a rest after experiencing a slowing down of $ = 0.05 rad/s 2 . a.) Over what angle (in radians) did the coin rotate? b.) What linear distance did the coin move? a) 90 rad b) 135 cm Centripetal Acceleration • Moving in circle at constant SPEED does not mean constant VELOCITY • Centripetal acceleration results from CHANGING DIRECTION of the velocity Centripetal Acceleration, cont. • Acceleration directed toward center of circle !...
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 Spring '06
 Pratt
 Physics, Circular Motion, Force, General Relativity, Velocity

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