# Another angular velocity problem

A Ferris wheel makes two rotations per minute. The radius of the Ferris wheel is 25 m.

a) Determine the angular velocity in rad/s
b) A ride lasts 4 min. How far will a rider travel in 4 min?

My Work:

a) C = 2Pi(25 m) = 50Pi m
50Pi m / 25 m = 2Pi rad

2 rotations/min x 2Pi = 4Pi rad/min

Therefore the angular velocity is Pi / 15 rad/s

b) 4 x 4Pi = 16Pi
16Pi = a / 25 m
a = 25(16Pi)
a = 400Pi
a = 1256.6 m

I believe I am correct but I am hoping someone could check over my approach to the problem as my text was not very clear at all and I have tried to figure this out mainly on my own.

HallsofIvy
Homework Helper
A Ferris wheel makes two rotations per minute. The radius of the Ferris wheel is 25 m.

a) Determine the angular velocity in rad/s
b) A ride lasts 4 min. How far will a rider travel in 4 min?

My Work:

a) C = 2Pi(25 m) = 50Pi m
50Pi m / 25 m = 2Pi rad
Why did you calculate this? Surely you knew from the start that there are $2\pi$ radians in any circle!

2 rotations/min x 2Pi = 4Pi rad/min

Therefore the angular velocity is Pi / 15 rad/s
Yes, although I think I would have said "one rotation in 30 seconds is $2\pi/30= \pi/15$ radians per second", this is fine.

b) 4 x 4Pi = 16Pi
16Pi = a / 25 m
a = 25(16Pi)
a = 400Pi
a = 1256.6 m
You had already calcuated in (a) (where it wasn't necessary!) that the circumference of the wheel is $50\pi$ meters. Now you calculate it again! In 4 minutes you will have made 8 rotations: $8(50\pi)= 400\pi$ m just as you say. I think I would leave it as $400\pi m$ and not change to an approximate answer.

I believe I am correct but I am hoping someone could check over my approach to the problem as my text was not very clear at all and I have tried to figure this out mainly on my own.
You've done some unnecessary work but you have the correct answers.