4 Solution Set 4 on chapters 8&9

4 Solution Set 4 on chapters 8&9 - 1 Chapter 8:...

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Chapter 8: Rotational Kinematics. Selected Conceptual Questions, pp.240. Problems pp. 241: # 13, 16, 25, 32, 40, 41, 52, 72 Chapter 9: Rotational Dynamics . Selected Conceptual Questions, pp.276. Problems pp. 277: # 5, 10, 12, 16, 19, 28, 37, 41, 46, 58, 72, 76 Chapter 8: Rotational Kinematics 13. REASONING AND SOLUTION The people meet at time t. At this time the magnitudes of their angular displacements must total 2 π rad. θ 1 + 2 = 2 rad Then ϖ 1 t + 2 t = 2 rad 3 3 1 2 2 rad 2 rad 1200 s 1.7 10 rad/s 3.4 10 rad/s t - - = = = + × + × 16. REASONING The time required for the bullet to travel the distance d is equal to the time required for the discs to undergo an angular displacement of 0.240 rad. The time can be found from Equation 8.2; once the time is known, the speed of the bullet can be found using Equation 2.2. SOLUTION From the definition of average angular velocity: t = the required time is 3 0.240 rad 2.53 10 s 95.0 rad/s t - ∆ = = = × Note that = because the angular speed is constant. The (constant) speed of the bullet can then be determined from the definition of average speed: 3 0.850 m 336 m/s 2.53 10 s x d v t t - = = = = × 1
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25. REASONING a. The time t for the wheels to come to a halt depends on the initial and final velocities, ϖ 0 and , and the angular displacement θ : ( 29 1 0 2 t = + (see Equation 8.6). Solving for the time yields 0 2 t = + b. The angular acceleration α is defined as the change in the angular velocity, - 0 , divided by the time t : 0 t - = (8.4) SOLUTION a. Since the wheel comes to a rest, = 0 rad/s. Converting 15.92 revolutions to radians (1 rev = 2 π rad), the time for the wheel to come to rest is 0 2 15.92 rev 2 t + = = + ( 29 2 rad 1 rev 10.0 s 20.0 rad/s 0 rad/s = + + b. The angular acceleration is 2 0 0 rad/s 20.0 rad/s 2.00 rad/s 10.0 s t - - = = = - ______________________________________________________________________________ 32. REASONING In addition to knowing the initial angular velocity 0 and the acceleration , we know that the final angular velocity is 0 rev/s, because the wheel comes to a halt. With values available for these three variables, the unknown angular displacement θ can be calculated from Equation 8.8 ( 29 2 2 0 2 αθ = + . When using any of the equations of rotational kinematics, it is not necessary to use radian measure. Any self-consistent set of units may be used to measure the angular quantities, such as revolutions for θ , rev/s for 0 and , and rev/s 2 for . A greater initial angular velocity does not necessarily mean that the wheel will come to a halt on an angular section labeled with a greater number. It is certainly true that greater initial angular velocities lead to greater angular displacements for a given deceleration. However, remember that the angular displacement of the wheel in coming to a halt may consist of a
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This note was uploaded on 04/01/2011 for the course PHY 135 taught by Professor Wagihghobriel during the Spring '11 term at University of Toronto- Toronto.

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4 Solution Set 4 on chapters 8&9 - 1 Chapter 8:...

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