Question

The propeller of an airplane is 9 feet in diameter. What is the speed of the tip of a propeller blade if the angular velocity of the propeller is 50 radians per second?

11 ft/sec
22.5 ft/sec
225 ft/sec

Answer 1

The speed of the tip of a propeller blade is
`225\, (ft)/(sec)`

Explanation:

Given

Angular velocity of the propeller ,
`\omega = 50 \, (radians)/(second)`

Diameter of propeller blade , D= 9 feet

Therefore radius of propeller blade ,
`R=(D)/(2)=4.5 feet`

Now speed of tip of blade ,
`v=\omega * R=50* 4.5(ft)/(sec)=225(ft)/(sec)`

Thus the speed of the tip of a propeller blade is
`225\, (ft)/(sec)`

Answer 2

speed = angular velocity * radius

angular velocity = 50
radius = diameter / 2 = 9/2

∴ speed = 50 * 9/2 = 225 ft/sec

The correct answer is the third option 225 ft/sec