F10P1AChap10Sol

F10P1AChap10Sol - Chapter 10 293 Rotational Motion...

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Chapter 10 293 Rotational Motion SOLUTIONS TO PROBLEMS Section 10.1 Angular Position, Speed, and Acceleration P10.1 (a) ! t = 0 = 5.00 rad t = 0 = d " dt t = 0 = 10.0 + 4.00 t t = 0 = 10.0 rad s # t = 0 = d dt t = 0 = 2 (b) t = 3.00 s = 5.00 + 30.0 + 18.0 = 53.0 rad t = 3.00 s = d dt t = 3.00 s = 10.0 + 4.00 t t = 3.00 s = 22.0 rad s t = 3.00 s = d dt t = 3.00 s = 2 Section 10.2 Rotational Kinematics ί The Rigid Object Under Constant Angular Acceleration P10.6 f " i = i t + 1 2 $ t 2 and f = i + t are two equations in two unknowns i and α i = f " t : f " i = f " t ( ) t + 1 2 t 2 = f t " 1 2 t 2 37.0 rev 2 rad 1 rev " # $ % & ' = 3.00 s ( ) ( 1 2 ) 3.00 s ( ) 2 232 rad = 294 rad ! 4.50 s 2 ( ) : = 61.5 rad 4.50 s 2 = 2
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294 Rotational Motion Section 10.3 Relations Between Rotational and Translational Quantities P10.8 Estimate the tire’s radius at 0.250 m and miles driven as 10 000 per year. ! = s r = 1.00 " 10 4 mi 0.250 m 1 609 m 1 mi # $ % & ' ( = 6.44 " 10 7 rad yr = 6.44 " 10 7 rad yr 1 rev 2 ) rad # $ % & ' ( = 1.02 " 10 7 rev yr or ~ 10 7 rev yr P10.9 (a) = 2 " f = 2 rad 1 rev 1 200 rev 60.0 s # $ % & ' ( = 126 rad s (b) v = r = 126 rad s ( ) 3.00 " 10 # 2 m ( ) = (c) a c = 2 r = 126 ( ) 2 8.00 " 10 # 2 ( ) = 1 260 m s 2 so r a r = 1.26 km s 2 toward the center (d) s = r = rt = ( ) 8.00 # 10 $ 2 m ( ) 2.00 s ( ) = 20.1 m Section 10.4 Rotational Kinetic Energy P10.14 m 1 = 4.00 kg , r 1 = y 1 = 3.00 m ; m 2 = 2.00 kg , r 2 = y 2 = 2.00 m ; m 3 = 3.00 kg , r 3 = y 3 = 4.00 m ; = 2.00 rad s about the x -axis (a) I x = m 1 r 1 2 + m 2 r 2 2 + m 3 r 3 2 I x = 4.00 3.00 ( ) 2 + 2.00 2.00 ( ) 2 + 3.00 4.00 ( ) 2 = 92.0 kg ! m 2 K R = 1 2 I x 2 = 1 2 92.0 ( ) 2.00 ( ) 2 = 184 J FIG. P10.14 (b) v 1 = r 1 = 3.00 2.00 ( ) = 6.00 m s K 1 = 1 2 m 1 v 1 2 = 1 2 4.00 ( ) 6.00 ( ) 2 = 72.0 J v 2 = r 2 = 2.00 2.00 ( ) = 4.00 m s K 2 = 1 2 m 2 v 2 2 = 1 2 2.00 ( ) 4.00 ( ) 2 = 16.0 J v 3 = r 3 = 4.00 2.00 ( ) = K 3 = 1 2 m 3 v 3 2 = 1 2 3.00 ( ) 8.00 ( ) 2 = 96.0 J K = K 1 + K 2 + K 3 = 72.0 + 16.0 + 96.0 = 184 J = 1 2 I x 2
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