1. Chp. 7 Rotational Motion

2. Rotational Motion When an object spins or moves about an axis of rotation it has rotational motion. Ɵ Ɵ = S = angular displacement the angle r of change in motion measured in radians in rotary motion S 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) _____ o x Π/180 o = Ɵ (in radians)

4. FYI: Linear vs. Rotational Kinematic Equations v f = v i + a Δ t x = v i t + ½ a Δ t 2 v f 2 = v i 2 + 2a Δ x x = ½ (v i +v f ) Δ t ω f = ω i + α Δ t Δ Ɵ = ω i Δ t+ ½ α Δ t 2 ω f 2 = ω i 2 + 2 α Δ Ɵ Δ Ɵ = ½(ω i +ω f ) Δ t * Table 7-2 page 251

5. Tangential Speed: V t (units: m/sec) Instantaneous linear speed of an object directed along a tangent path to an object’s circular motion. v t = r ω Tangential Acceleration: a t (units: m/sec 2 ) Instantaneous linear acceleration of an object along it’s tangent path to the object’s circular motion. a t = r α * Sample 7E & 7F page 254 & 256

6. Centripetal Acceleration: a c Accleration due to change in direction and it is directed toward the center of the circular path. a t vs. a c : They are not the same thing!! a t vs. a c : They are not the same thing!! a c = v t 2 ( units: m/s 2 ) r a c = r ω 2 (units: m x (rad/s) 2 = m/s 2 ) a c = v t 2 ( units: m/s 2 ) r a c = r ω 2 (units: m x (rad/s) 2 = m/s 2 )

7. acac atat a total a total = a c 2 + a t 2 Therefore… tan Ɵ = a c a t * Sample 7G page 258

8. Forces that create and maintain circular motion F c = ma c = mv t 2 = mr ω 2 (units: N) r FcFc m V r Centripetal Force *Sample 7H page 261

9. Newton’s Law of Universal Gravitation 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. Universal Gravitation Constant G= 6.673 x 10 -11 N m 2 /kg 2 F g = G m 1 m 2 r 2

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

11. 7E 1,2,4 2. ω 1 =10.5 rad/s 4. a. 3.6m/s b. 15 rad/s c. 29 m/s d. 1.3m 7F 1,2,32. r =.51m 7G 1,2,52. v t =11 m/s 7H 1,3,4 4. v t = 35 m/s 7 I 1,2,32. r = 9.4 x 10 6 m ?? Km Hmwk. #3 Book Chp. 7

12. Hmwk. #4 WKBK 7E 1. r = 1 m 2. circumference = 5520 km 3. r =.025m = ??cm 5. v t =.243 m/s 7F 1. α = 6.2 x 10 -3 rad/s 2 3. r = 40m 5. a t = 28m/s 2 7G 2. r = 50.1 m 3. v t =.158 m/s 4. v t =.013 m/s 7H 1. v t = 12.3 m/s 2. v t = 2.8 m/s 4. r = 3.17km 7I 1. m 2 = 5 x 10 15 kg 2. m 2 = 2.26 x 10 4 kg