An airplane is flying above the Earth's surface at a height of 10.9 km. The centripetal acceleration of the plane is 16.7 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.

To find the angular velocity of the plane moving in uniform circular motion, we need to relate the centripetal acceleration to the angular velocity.

First, let's define the given values:

Height of the plane above the Earth's surface (h): 10.9 km
Centripetal acceleration (a): 16.7 m/s^2
Radius of the Earth (r): 6400 km = 6,400,000 m

To start, we need to find the total radius of the circular path along which the plane is flying. This is the sum of the radius of the Earth and the height of the plane above the surface:

Total radius (R) = radius of the Earth + height of the plane
R = r + h

Now we can find the angular velocity (ω) using the equation:

a = Rω²

Rearranging the equation, we have:

ω = √(a/R)

Now let's substitute the given values:

R = 6,400,000 + 10,900 = 6,410,900 m

ω = √(16.7 / 6,410,900)

Calculating the square root and dividing 16.7 by 6,410,900, we get:

ω ≈ 0.0419 rad/s

Therefore, the angular velocity of the plane moving in uniform circular motion is approximately 0.0419 rad/s.