2 Therefore the angular displacement is equal to the product of the average

# 2 therefore the angular displacement is equal to the

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elapsed time (Equation 8.2). Therefore, the angular displacement is equal to the product of the average angular velocity and the elapsed time The elapsed time is given, so we need to determine the average angular velocity. We can do this by using the graph of angular velocity versus time that accompanies the problem. SOLUTION The angular displacement is related to the average angular velocity and the 3.0 s 8.0 s +15 rad/ s –9.0 rad/ s 0 Time (s) Angular velocity +3.0 rad/s  Since the angular displacement is zero, 0 = – . Solving 0 t (Equation 8.4) for t and using the fact that 0 = – give t 2 2( 25.0 rad/s) 4.00 rad/s 2 12.5 s 33. REASONING The angular displacement of the child when he catches the horse is, from Equation 8.2, c c t . In the same time, the angular displacement of the horse is, from Equation 8.7 with 0 0 rad/s, h 1 2 t 2 . If the child is to catch the horse c h ( / 2) . SOLUTION Using the above conditions yields 2 1 1 c 2 2 0 t t or 2 2 1 1 2 2 (0.0100 rad/s ) 0.250 rad/s rad 0 t t The quadratic formula yields t = 7.37 s and 42.6 s; therefore, the shortest time needed to catch the horse is t = 7.37 s .  #### You've reached the end of your free preview.

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