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Unformatted text preview: CHAPTER 8 ROTATIONAL KINEMATICS ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1. (d) Using Equation 8.1 ( = Arc length / Radius) to calculate the angle (in radians) that each object subtends at your eye shows that Moon = 9.0 10 3 rad, Pea = 7.0 10 3 rad, and Dime = 25 10 3 rad. Since Pea is less than Moon , the pea does not completely cover your view of the moon. However, since Dime is greater than Moon , the dime does completely cover your view of the moon. 2. 2.20 cm 3. 38.2 s 4. (a) An angular acceleration of zero means that the angular velocity has the same value at all times, as in statements A or B. However, statement C is also consistent with a zero angular acceleration, because if the angular displacement does not change as time passes, then the angular velocity remains constant at a value of 0 rad/s. 5. (c) A non-zero angular acceleration means that the angular velocity is either increasing or decreasing. The angular velocity is not constant. 6. (b) Since values are given for the initial angular velocity , the final angular velocity , and the time t , Equation 8.6 [ ( 29 1 2 t = + ] can be used to calculate the angular displacement . 7. 32 rad/s 8. 88 rad 9. (c) According to Equation 8.9 ( v T = r ), the tangential speed is proportional to the radius r when the angular speed is constant, as it is for the earth. As the elevator rises, the radius, which is your distance from the center of the earth, increases, and so does your tangential speed. 10. (b) According to Equation 8.9 ( v T = r ), the tangential speed is proportional to the radius r when the angular speed is constant, as it is for the merry-go-round. Thus, the angular speed of the second child is ( 29 T 2.1 m 2.2 m/s 1.4 m v = . 136 ROTATIONAL KINEMATICS 11. 367 rad/s 2 12. (e) According to Newtons second law, the centripetal force is given by c c F ma = , where m is the mass of the ball and a c is the centripetal acceleration. The centripetal acceleration is given by Equation 8.11 as a c = r 2 , where r is the radius and is the angular speed. Therefore, 2 c F mr = , and the centripetal force is proportional to the radius when the mass and the angular speed are fixed, as they are in this problem. As a result, ( 29 c 33 cm 1.7 N 12 cm F = . 13. (d) Since the angular speed is constant, the angular acceleration is zero, according to Equation 8.4. Since = 0 rad/s 2 , the tangential acceleration a T is zero, according to Equation 8.10. The centripetal acceleration a c , however, is not zero, since it is proportional to the square of the angular speed, according to Equation 8.11, and the angular speed is not zero....
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- Fall '11