An airplane is flying above the Earth's surface at a height of 9.30 km. The centripetal acceleration of the plane is 18.2 m/s2. What is the angular velocity of the plane moving in uniform circular motion? Take the radius of the earth to be 6400 km.
so, what is the formula for centripetal acceleration?
Just plug in your numbers to find ω.
To find the angular velocity of the airplane, we can use the formula:
angular velocity (ω) = centripetal acceleration (a) / radius (r)
First, let's convert the height of the plane from kilometers to meters:
Height of the plane = 9.30 km * 1000 m/km = 9300 m
Next, we need to convert the radius of the Earth from kilometers to meters:
Radius of the Earth = 6400 km * 1000 m/km = 6,400,000 m
Now we can plug in the values into the formula:
ω = 18.2 m/s^2 / (6,400,000 m + 9,300 m)
Simplifying the denominator:
ω = 18.2 m/s^2 / 6,409,300 m
Calculating the angular velocity:
ω ≈ 2.8432 × 10^(-6) rad/s
Therefore, the angular velocity of the airplane moving in uniform circular motion is approximately 2.8432 × 10^(-6) rad/s.