Respuesta :
If a Ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute then the acceleration of a passenger at his lowest point during the ride is 4.11 [tex]\text{m/s}^{2}[/tex].
Calculation:
Step-1:
It is given that the radius of the Ferris wheel is r=15 m, and the angular speed of the wheel is [tex]\omega[/tex]=5rev/min.
It is required to find the angular acceleration of a passenger at his lowest point during the ride.
The formula required to calculate the angular acceleration is, [tex]a=\omega ^2 r[/tex].
Step-2:
Now substituting the given values into the equation to get the value of the angular acceleration.
[tex]\begin{aligned}a &=\omega^{2} r \\&=(5 \mathrm{rev} / \mathrm{min})^{2}(15 \mathrm{~m}) \\&=\left(5 \mathrm{rev} / \mathrm{min} \times \frac{\left(\frac{2 \pi}{60}\right) \mathrm{rad} / \mathrm{sec}}{1 \mathrm{rev} / \mathrm{min}}\right)^{2}(15 \mathrm{~m}) \\&=(0.2741 \times 15) \mathrm{m} / \mathrm{s}^{2} \\&=4.11 \mathrm{~m} / \mathrm{s}^{2}\end{aligned}[/tex]
The acceleration is towards upwards that means towards the center of the wheel.
Learn more about the angular acceleration:
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