A point on the rim of a 0.25-m radius fan blade has centripetal acceleration of 0.20 m/s2. Find the centripetal acceleration of a point 0.1 m from the center of the same wheel.Select one:a.0.01 m/s2b.0.02 m/s2c.0.08 m/s2d.0.04 m/s2
Question
A point on the rim of a 0.25-m radius fan blade has centripetal acceleration of 0.20 m/s2. Find the centripetal acceleration of a point 0.1 m from the center of the same wheel.Select one:a.0.01 m/s2b.0.02 m/s2c.0.08 m/s2d.0.04 m/s2
Solution
The centripetal acceleration (a) of a point in circular motion is given by the formula a = ω²r, where ω is the angular velocity and r is the radius of the circle.
Given that a point on the rim of the fan blade (r = 0.25 m) has a centripetal acceleration of 0.20 m/s², we can find the angular velocity using the formula:
ω = sqrt(a/r) = sqrt(0.20 m/s² / 0.25 m) = sqrt(0.8 s⁻²) = 0.894 s⁻¹
Now, to find the centripetal acceleration of a point 0.1 m from the center of the wheel, we substitute r = 0.1 m into the formula:
a = ω²r = (0.894 s⁻¹)² * 0.1 m = 0.08 m/s²
So, the answer is c. 0.08 m/s².
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