A Ferris wheel has a radius of 30 feet and travels 6.8 feet every second. At what constant angular speed does the Ferris wheel rotate at (in radians per second)?
______radians per second
A Ferris wheel has a radius of 26 feet and travels 2 radians every 4 seconds. At what constant angular speed does the Ferris wheel rotate at (in radians per second)?
________radians per second
Why did the Ferris wheel go to therapy? It had trouble rotating in circles and needed some guidance!
For the first question, to find the angular speed in radians per second, we can use the formula:
angular speed = linear speed / radius
So, for the first Ferris wheel with a radius of 30 feet and traveling 6.8 feet every second, the angular speed is:
angular speed = 6.8 feet/second / 30 feet = 0.2267 radians/second
For the second question, to find the angular speed in radians per second, we can use the formula:
angular speed = angle / time
So, for the second Ferris wheel with a radius of 26 feet and traveling 2 radians every 4 seconds, the angular speed is:
angular speed = 2 radians / 4 seconds = 0.5 radians/second
I hope these answers rotate your world!
To find the constant angular speed of the Ferris wheel in radians per second, we can use the formula:
Angular speed = Distance traveled / Time taken
For the first question, we're given:
Radius = 30 feet
Distance traveled = 6.8 feet
Time taken = 1 second
Plugging these values into the formula, we get:
Angular speed = 6.8 feet / 1 second
Therefore, the constant angular speed of the Ferris wheel is 6.8 radians per second.
For the second question, we're given:
Radius = 26 feet
Distance traveled = 2 radians
Time taken = 4 seconds
Plugging these values into the formula, we get:
Angular speed = 2 radians / 4 seconds
Therefore, the constant angular speed of the Ferris wheel is 0.5 radians per second.
To find the constant angular speed in radians per second, we need to divide the distance traveled by the radius.
For the first question:
Distance traveled = 6.8 feet
Radius of the Ferris wheel = 30 feet
Angular speed (in radians per second) = Distance traveled / Radius
Angular speed = 6.8 feet / 30 feet
To convert the angular speed from feet to radians, we need to multiply it by the conversion factor of 1 radian = 1 foot / radius.
Angular speed = (6.8 feet / 30 feet) * (1 radian / 1 foot)
Angular speed = 0.2267 radians per second
So, the constant angular speed of the Ferris wheel is approximately 0.2267 radians per second.
For the second question:
Distance traveled = 2 radians
Radius of the Ferris wheel = 26 feet
Angular speed (in radians per second) = Distance traveled / Radius
Angular speed = 2 radians / 26 feet
To convert the angular speed from feet to radians, we need to multiply it by the conversion factor of 1 radian = 1 foot / radius.
Angular speed = (2 radians / 26 feet) * (1 radian / 1 foot)
Angular speed = 0.0769 radians per second
So, the constant angular speed of the Ferris wheel is approximately 0.0769 radians per second.
It takes 30*2π/6.8 = 27.72 seconds to make one revolution. That is an angular speed of
2πrad/27.72s = 0.2267 rad/s
ω = 2π rad / (2π*30ft * 1s/6.8ft) = 1/(30/6.8) = 0.2267 rad/s
Do the other in like wise.