A ventilation fan has blades 0.25 m long rotating at 20 rpm. What is the centripetal acceleration of a point on the outer tip of a blade?Select one:a.0.87 m/s2b.0.55 m/s2c.1.1 m/s2d.0.23 m/s2
Question
A ventilation fan has blades 0.25 m long rotating at 20 rpm. What is the centripetal acceleration of a point on the outer tip of a blade?Select one:a.0.87 m/s2b.0.55 m/s2c.1.1 m/s2d.0.23 m/s2
Solution
The centripetal acceleration (a) can be calculated using the formula:
a = rω²
where r is the radius (in this case, the length of the fan blade) and ω is the angular velocity.
First, we need to convert the angular velocity from revolutions per minute (rpm) to radians per second.
1 revolution = 2π radians 1 minute = 60 seconds
So, 20 rpm = 20 * (2π/60) = 2π/3 rad/s
Now we can substitute r and ω into the formula:
a = 0.25 m * (2π/3 rad/s)²
a = 0.25 m * (4π²/9) rad²/s²
a = π²/9 m/s²
a ≈ 1.1 m/s²
So, the correct answer is c. 1.1 m/s².
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