if a Ferris wheel with a radius of 22 feet takes 25 seconds to turn 4(pi)/5 radians, find the angular speed of the wheel! please help asap
4π/5 rad / 25s = 4π/125 rad/s
or 2/125 rev/s
The radius of the wheel does not matter
To find the angular speed of the Ferris wheel, you can use the formula:
Angular speed = θ / t
Where:
- θ is the angle (in radians) through which the wheel turns
- t is the time (in seconds) it takes to turn through that angle
Given that the wheel turns through an angle of 4π/5 radians in 25 seconds, we can substitute these values into the formula:
Angular speed = (4π/5) / 25
To simplify, divide both the numerator and denominator by 5:
Angular speed = (4π/5) / 25 = (4π) / (5 * 25)
Simplifying further, we have:
Angular speed = 4π / 125
So, the angular speed of the ferris wheel is 4π/125 radians per second.
To find the angular speed of the Ferris wheel, we need to first understand the relationship between angular speed and time.
Angular speed (ω) is the rate of change of an angle with respect to time. It is measured in radians per second (rad/s). The formula for angular speed is:
ω = θ / t
where ω is the angular speed, θ is the angle in radians, and t is the time in seconds.
In this case, the Ferris wheel rotates a certain angle (θ) in a given time (t). The angle is given as 4(pi)/5 radians, and the time is 25 seconds. So, we can substitute these values into the formula to find the angular speed:
ω = (4(pi)/5) / 25
To evaluate this expression, we need to convert π to a decimal approximation. Let's use 3.14 for π:
ω = (4(3.14)/5) / 25
= (12.56/5) / 25
= 2.512 / 25
= 0.10048 rad/s (rounded to five decimal places)
Therefore, the angular speed of the Ferris wheel is approximately 0.10048 rad/s.