Trig Problem: Angular Velocity.

[Senjai]

Homework Statement

A Ferris Wheel with a radius of 25.3m makes two rotations per minute.

A) Find the average angular speed of the Ferris wheel in radians per second.

B) How far does a rider travel if the ride lasts 5 minutes?

The Attempt at a Solution

A) I got this question after a little bit of trial and error. i stated one rotation was 360 degrees which is equivalent to $$2\pi$$ Radians. It rotated twice per minute, so i stated that it rotated $$4\pi$$ radians per minute, my final equation to solve for the angular velocity was:

$$\frac{4\pi}{60} \cong 0.21 radians$$

B) I can't seem to get this answer. My answer is 794.82, if i multiply it by 2 i get the correct answer so i don't understand where I am missing the 2. the correct answer is 1590 m.

i started with this equation

$$\frac{10\pi}{2\pi} = \frac{d}{2\pi r}$$

after some mismatching i canceled out the common term of 2 pi on both sides and got:

$$d = 10\pi r$$ which yields the aforementioned answer. Does anyone know what I'm missing?

Thanks,

Senjai

 

[danago]

One full rotation would cover a distance of $$2\pi r$$ meters.

With a rate of two rotations per minute, a total of 10 rotations is made in 5 minutes.

Hence, the total distance traveled is $$2\pi r * 10$$ which yields the required answer.Im not 100% sure where that equation you wrote came from ( $$\frac{10\pi}{2\pi} = \frac{d}{2\pi r}$$), but i suspect that the $$10\pi$$ should be $$20\pi$$, the total angle covered?

 

[Senjai]

I got that equation from the fact the sector angle is proportional to an increase in sector or arc. But i understand where your coming from. Thanks for all your help!