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Introductory Physics Homework Help
Angular speed, acceleration, and angle of a Ferris wheel
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[QUOTE="ac7597, post: 6253000, member: 667255"] [B]Homework Statement:[/B] The county fair features a big Ferris Wheel of radius R=8 m. The drive mechanism is designed to accelerate the wheel from rest to a maximum angular speed ω=1.3 radians per second in a gradual manner: the angular speed at any time t is given by: ω(t)=(1.3)∗(1.0−e^(−t/τ) ) where t is the time in seconds since the ride started, and τ=22 seconds is the so-called "time constant" of the ride; it indicates roughly the time it takes for the ride to change its speed significantly. What is the angular speed ω of the Ferris Wheel at time t=10 seconds after it has started from rest? What is the angular acceleration at time t=10 seconds? What is the total angle by which the wheel rotates over this period of t=10 seconds? How long does it take the wheel to complete its first revolution as it starts from rest? [B]Relevant Equations:[/B] ω(t)=(1.3)∗(1.0−e^(−t/τ) ) ω(10)=(1.3)∗(1.0−e^(−10/22) )= 0.475 rad/s 0.475 rad/s=0 +α(10second) α=0.0475 rad/s^2 ∫ω(t)=Θ =1.3t + 28.6e^(-t/22) | (t=10s, t=0) total angle by which the wheel rotates over this period of t=10 seconds = 2.55 rad Θ= 2(pi)(8m)= 1.3t + 28.6e^(-t/22) 0=1.3t + 28.6e^(-t/22) - 2(pi)(8m) t=34 seconds [/QUOTE]
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Introductory Physics Homework Help
Angular speed, acceleration, and angle of a Ferris wheel
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