A ferris wheel rotates at an angular velocity of .036 rad/s. At t=0min your friend Seth is at the very top of the ride. What is Seth's angular position at t=3 min, measured counterclockwise from the top?
the wheel spins counterclockwise
Well, isn't your friend Seth quite the daredevil! Alright, let's calculate his angular position at t=3 minutes.
We know that the angular velocity (ω) of the ferris wheel is 0.036 rad/s. To find Seth's angular position (θ), we can use the formula:
θ = ω × t,
where θ is the angular position, ω is the angular velocity, and t is the time.
Plugging in the values, we have:
θ = 0.036 rad/s × 3 min,
First, let's convert minutes to seconds, because our angular velocity is in rad/s:
3 min = 3 × 60 sec = 180 sec.
Now, let's calculate Seth's angular position:
θ = 0.036 rad/s × 180 sec.
And if you do the math, you'll find that Seth's angular position at t=3 minutes is 6.48 radians counterclockwise from the top.
So, I hope Seth enjoys the view from his lofty position while the ferris wheel keeps spinning!
To find Seth's angular position at t = 3 min, first, we need to determine the angular distance he has traveled in that time.
Angular distance (θ) is given by the formula: θ = ωt, where ω is the angular velocity and t is the time.
Given:
Angular velocity (ω) = 0.036 rad/s
Time (t) = 3 min = 3 * 60 = 180 seconds
θ = ωt
θ = 0.036 rad/s * 180 s
θ = 6.48 radians
Now, since Seth is initially at the very top of the ride, his angular position at t = 3 min, measured counterclockwise from the top, is 6.48 radians.
To find Seth's angular position at t = 3 minutes, we need to determine how many radians he has traveled counterclockwise from the top of the ferris wheel.
First, let's calculate the angle covered in 3 minutes:
Angular velocity (ω) = 0.036 rad/s
Time (t) = 3 minutes = 3 * 60 = 180 seconds
Angular displacement (θ) = ω * t
= 0.036 rad/s * 180 s
= 6.48 radians
Since Seth is at the very top of the ride at t = 0 minutes, his angular position at t = 3 minutes will be 6.48 radians counterclockwise from the top.
Dooes the wheel spin counterclockwise? I assume it does.Otherwise subtract the answer from 2 pi
.036 radians/second * 180 seconds = 6.48 radians
a full circle is 2 pi = 6.28 radians
so it is a full circle + .2 radians