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10_InstSolManual_PC

# 10_InstSolManual_PC - ROTATIONAL MOTION 10 EXERCISES...

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10.2 Chapter 10 D EVELOP Given a constant angular acceleration α , the angular velocity and angular position at a later time t can be found using Equations 10.7 and 10.8: 0 2 0 0 1 2 t t t ϖ ϖ α θ θ ϖ α = + = + + E VALUATE (a) The initial and final angular velocities are 0 0 ϖ = and 3600 rev 2 (3600) rad 3600 rpm 377 rad/s 1 min 60 s π ϖ = = = = Therefore, the amount of time it takes to reach this angular speed is 0 2 377 rad/s 0 725 s 12.1 min 0.52 rad/s t ϖ ϖ α - - = = = = (b) Using Equation 10.8, we find the number of turns made during this time interval to be 2 2 2 2 5 4 0 0 1 1 1 (0.52 rad/s )(725 s) 1.37 10 rad 2.17 10 rev 2 2 2 t t t θ θ ϖ α α = + + = = = × = × A SSESS The turbine turns very fast. After 12.1 min, it has reached an angular speed of 377 rad/s, or 60 rev/s!
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