H-sol - Chapter H - Problems Blinn College - Physics 2425 -...

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Unformatted text preview: Chapter H - Problems Blinn College - Physics 2425 - Terry Honan Problem H.1 A wheel rotates from rest to 12 rad s in 3 s. Assume the angular acceleration is constant. (a) What is the magnitude of the wheel's angular acceleration? (b) Through what angle (in radians) does the wheel rotate? Solution to H.1 H a L w = w + a t 12 = + a 3 a = 4 rad s H b L Dq = 1 2 I w + w M t = 1 2 H + 12 L 3 = 18 rad Problem H.2 (a) What is the angular velocity of the Earth in its orbit about the Sun. (b) What is the angular velocity of the Moon in its orbit about the Earth. Solution to H.2 A constant angular velocity is related to the period T by w = 2 p T . H a L T = 1 year = 365.24 24 3600 = 3.1557 10 7 s w = 1.99 10- 7 rad s H b L T = 27.32 days = 27.32 24 3600 = 2.36 05 10 6 s w = 2.66 10- 6 rad s Problem H.3 A grinding wheel rotating at 100 rev min is turned off. It slows with a constant angular acceleration of 2 rad s. (a) How long does it take the wheel to stop? (b) Through what angle, in radians, does it turn while slowing? Solution to H.3 w = and w = 100 rev min 2 p rad rev 1 min 60 s = 10.472 rad s H a L w = w + a t = 10.472- 2 t 5.24 s H b L w 2- w 2 = 2 a Dq Dq =- 10.472 2 2 2 = 27.4 rad Problem H.4 A car races around a circular track of radius 250 m at a constant speed of 45 m s . (a) What is its angular velocity? (b) What is the magnitude and direction of its acceleration? Solution to H.4 R = 250 m and v = 45 m H a L v = r w w = v R = 0.18 rad s H b L a c = w 2 r = v 2 R = 8.1 m s 2 The direction of the acceleration is centripetal, meaning that is directed toward the center. Problem H.5 By rotating through 1.25 rev of a 1 m radius arc, a discus thrower uniformly accelerates a discus from rest to 25 m s . (a) What is the final angular velocity of the discus? (b) What is its angular acceleration? (c) What is the total time of acceleration? Solution to H.5 H a L v = r w w = v r = 25 1 = 25 rad s H b L w 2-w 2 = 2 a Dq 25 2- = 2 a H 2 p 1.25 L a = 39.8 rad s H c L Dq = 1 2 I w + w M t 2 p 1.25 = 1 2 H + 25 L t t = 0.628 s Problem H.6 Assume that a baseball is a uniform sphere of radius 3.80 cm. If it moves at a speed of 38 m s (the speed of the center of mass) and rotates at 125 rad s then what is the ratio of the rotational kinetic energy to the translational kinetic energy. Solution to H.6 For a uniform solid sphere I = 2 5 M R 2 K rot = 1 2 I w 2 = 1 2 2 5 M R 2 w 2 = 1 5 M R 2 w 2 K rot K trans = 1 5 M R 2 w 2 1 2 M v 2 = 2 R 2 w 2 5 v 2 2 Chapter H - Problems Insert the numbers: R = 0.038 m , v = 38 m s and w = 125 rad s giving K rot K trans = 0.00625 . Problem H.7 Three masses glued onto a light rigid sheet in the xy plane. The masses and positions are: 4 kg at H- 3 m, 5 m L , 6 kg at H 4 m, 0 L and 8 kg at H 0,- 3 m L ....
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H-sol - Chapter H - Problems Blinn College - Physics 2425 -...

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