Final answer:
To find the centripetal acceleration and express it as a multiple of g, use the formula ℓ = v²/r and then divide by g to get the ratio. For example, a centripetal acceleration of 1.25 m/s² results in a ratio of 0.128g.
Step-by-step explanation:
To calculate the magnitude of the centripetal acceleration at the edge of a rotating object and compare it to the acceleration due to gravity (g = 9.8 m/s²), you can use the formula for centripetal acceleration, which is ℓ = v² / r, where ℓ is the centripetal acceleration, v is the linear velocity, and r is the radius of the circular path.
For example, if we know the linear velocity at the tip of a propeller and the radius, we can substitute these values into the formula to find ℓ. Then, to express this centripetal acceleration as a multiple of g, we would take the ratio ℓ/g. If ℓ is 1.25 m/s², then the ratio would be (1.25 m/s²) / (9.80 m/s²) = 0.128, which means the centripetal acceleration is 0.128g.