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Unformatted text preview: Chapter 7 Chapter 7 Rotational Motion Universal Law of Gravitation Keplers Laws Angular Displacement Angular Displacement Circular motion about AXIS Three measures of angles: 3. Degrees 4. Revolutions (1 rev. = 360 deg.) 5. Radians (2 rad.s = 360 deg.) Angular Displacement, cont. Angular Displacement, cont. Change in distance of a point: s = = Example 7.1 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 Angular Speed Can be given in Revolutions/s Radians/s > Called Degrees/s Linear Speed at r = f q i t inradians v = =  v = Example 7.2 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 Angular Acceleration Denoted by must be in radians per sec. Units are rad/s Every point on rigid object has same and = f w i t Rotational/Linear Equivalence: Rotational/Linear Equivalence: x w v w f v f a a t t Linear and Rotational Motion Linear and Rotational Motion Analogies Analogies Rotational Motion Linear Motion = + w f ( ) 2 t = t + 1 2 a t 2 f = w + a t f 2 2 = w 2 2 + a D q = f t 1 2 a t 2 x = v + v f ( ) 2 t v f = + x = v t + 1 2 at 2 x = v f t 1 2 at 2 v f 2 2 = + Example 7.3 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 Linear movement of a rotating point Distance Speed Acceleration Only works for angles in radians! Different points have different linear speeds! x = v = a = Example 7.4 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 ....
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This note was uploaded on 07/25/2008 for the course PHY 231C taught by Professor Pratt during the Spring '06 term at Michigan State University.
 Spring '06
 Pratt
 Physics, Circular Motion

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