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Chp . 7 Rotational Motion

Chp . 7 Rotational Motion. Rotational Motion. When an object spins or moves about an axis of rotation it has rotational motion. Ɵ = S = angular displacement the angle r of change in motion measured in radians in rotary motion. S. Ɵ. S = arc length , distance along the

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Chp . 7 Rotational Motion

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  1. Chp. 7 Rotational Motion

  2. Rotational Motion When an object spins or moves about an axis of rotation it has rotational motion. Ɵ = S=angular displacement the angle rof change in motion measured in radians in rotary motion S Ɵ S = arc length, distance along the circular path measured in m or cm r = radius of circular path, measured in m or cm • Fig, 7-3 • page 245

  3. Conversion: degrees to radians • Ɵ(in degrees) _____ox Π/180o = Ɵ(in radians)

  4. FYI:Linear vs. Rotational Kinematic Equations vf= vi+ aΔt x = vit + ½ aΔt2 vf2= vi2 + 2aΔx x = ½ (vi+vf)Δt ωf = ωi+αΔt ΔƟ = ωiΔt+ ½ αΔt2 ωf2 = ωi2+ 2αΔƟ ΔƟ = ½(ωi+ωf)Δt * Table 7-2 page 251

  5. Tangential Speed: Vt(units: m/sec) Instantaneous linear speed of an object directed along a tangent path to an object’s circular motion. vt= rω Tangential Acceleration: at(units: m/sec2) Instantaneous linear acceleration of an object along it’s tangent path to the object’s circular motion. at= rα * Sample 7E & 7F page 254 & 256

  6. Centripetal Acceleration: ac Accleration due to change in direction and it is directed toward the center of the circular path. ac = vt2( units: m/s2 ) r ac =rω2 (units: m x (rad/s)2 = m/s2 ) atvs. ac : They are not the same thing!!

  7. ac at atotal atotal =ac2 + at2 Therefore… tan Ɵ= ac at * Sample 7G page 258

  8. Forces that create and maintain circular motion Fc m r V Fc = mac= mvt2 = mrω2 (units: N) r Centripetal Force *Sample 7H page 261

  9. Newton’s Law of Universal Gravitation Based on the mutual force of attraction between particles of matter -- gravitational forces. Gravitational forces exist between any 2 objects no matter how small or how large or how far apart they are. Fg= G m1m2 r2 Universal Gravitation Constant G= 6.673 x 10-11 N m2/kg2

  10. * Sample 7I page 264 Satellites Pages 266-267 Calculating the escape speed for satellites: Vesc Vesc= 2MG R

  11. Hmwk. #3 Book Chp. 7 7E 1,2,4 2. ω1=10.5 rad/s 4. a. 3.6m/s b. 15 rad/s c. 29 m/s d. 1.3m 7F 1,2,3 2. r = .51m 7G 1,2,5 2. vt=11 m/s 7H 1,3,4 4. vt= 35 m/s 7 I 1,2,3 2. r = 9.4 x 106m ?? Km

  12. Hmwk. #4 WKBK 7E 1. r = 1 m 2. circumference = 5520 km 3. r = .025m = ??cm 5. vt= .243 m/s 7F 1. α = 6.2 x 10-3 rad/s2 3. r = 40m 5. at = 28m/s2 7G 2. r = 50.1 m 3. vt = .158 m/s 4. vt=.013 m/s 7H 1. vt = 12.3 m/s 2. vt= 2.8 m/s 4. r = 3.17km 7I 1. m2 = 5 x 1015kg 2. m2 = 2.26 x 104kg

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