Question

The tip of a fan blade is 0.61 m from the center of the fan. the fan turns at a constant speed and completes 2 rotations every 1.0 s. what is the centripetal acceleration of the tip of the fan blade?

Answer 1

The centripetal acceleration of the tip of the fan blade is 96.23 m/s²

What is centripetal acceleration?

The acceleration developed when a body is moving in circular way, directed towards the center of the circular path.

The tip of a fan blade is 0.61 m from the center of the fan. the fan turns at a constant speed and completes 2 rotations every 1.0 s

ac = ω²r

where ω = angular speed = 2πN/60, N = Rotation per minute

From the question, N = 2 x 60/1 = 120  RPM

So, the angular speed will be

ω = 2π x 120 /60

ω  = 12.56 rad/s

Then, the centripetal acceleration is

ac =  (12.56)² x   0.61 m

ac = 96.23 m/s²

Thus, centripetal acceleration of the tip of the fan blade is 96.23 m/s²

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