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 Homework Statement:

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 socalled "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?
 Relevant Equations:
 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
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