The Colossus ferris wheel at Six Flags St. Louis has a diameter of 50.3 m. A rider located on the circumference of the ferris wheel rotates at a speed of 16 km/h.
(a) What is the angular speed of the ferris wheel, in rad/sec?
(b) How long does it take for the ferris wheel to go through one full rotation?
(c) There is a bird sitting on the mid-span of one
of the ferris wheel support beams. How fast is the bird moving, in km/h?
d
(a) v = rω
You have v and r, so plug 'em in
(b) ω = 2πf ... the period t = 1/f
(c) halfway out, half the speed.
im confused on what does f represent
f is the frequency. That is, how many revolutions per hour (or minute, or whatever)
Looks like you have some studying to do, if even that is confusing.
To find the answers to these questions, we need to use some basic principles of circular motion.
(a) To find the angular speed of the ferris wheel in rad/sec, we can use the formula:
Angular Speed (in rad/sec) = Linear Speed (in m/s) / Radius (in meters)
First, let's convert the linear speed from km/h to m/s. There are 1000 meters in a kilometer, and 1 hour is equivalent to 3600 seconds. So:
Linear Speed (in m/s) = 16 km/h × (1000 m/1 km) × (1 h/3600 s) = (16 × 1000)/(3600) m/s = 4.44 m/s
Now, we can substitute the values into the formula:
Angular Speed (in rad/sec) = 4.44 m/s / (50.3 m / 2) = 4.44 m/s / 25.15 m = 0.176 rad/sec
Therefore, the angular speed of the ferris wheel is approximately 0.176 rad/sec.
(b) To find the time it takes for the ferris wheel to go through one full rotation, we can use the formula:
Time = 2π / Angular Speed
Substituting the value of angular speed we found in part (a):
Time = 2π / 0.176 rad/sec ≈ 35.8 seconds
So, it takes approximately 35.8 seconds for the ferris wheel to complete one full rotation.
(c) To find the speed of the bird, we need to consider that it is situated on the mid-span of one of the ferris wheel support beams. This means that the distance traveled by the bird is equal to the circumference of the ferris wheel.
Circumference = 2π × Radius = 2π × (50.3 m / 2) = 157.8 m
To convert this distance to km, we divide it by 1000:
Distance (in km) = 157.8 m / 1000 = 0.1578 km
Now, we can use the formula:
Speed (in km/h) = Distance (in km) / Time (in hours)
Substituting the distance traveled and the time it takes for one full rotation:
Speed (in km/h) = 0.1578 km / 0.0167 hours ≈ 9.45 km/h
Therefore, the bird is moving at approximately 9.45 km/h.