Answer:
1.789
Explanation:
let the tangential velocity at the tip of the blade (7.17m from center) be V₁ and the tangential velocity at 4.01 be V₂.
recall that tangential velocity can be related to angular velocity, ω by the following relationship:
V = rω, where V is the tangential velocity, ω is angular velocity and r = radius.
rearranging, we get
ω = V/r
We also know that at any point in the rotation, even though the tangential velocity at 7.17m radius (V₁) will be different from the tangential velocity at 4.01m radius (V₂), their angular velocity will be the same, hence we can equate:
ω₁ = ω₂, or
V₁/r₁ = V₂/r₂ (rearranging)
V₁/V₂ = r₁/r₂ -----(eq 1)
We also know that centripetal acceleration can be expressed in terms of tangential velocity and radius, i.e
a =V²/r
to find the ratio of the centripetal acceleration at the tip and at r=4.01m
a₁/a₂ = (V₁²/r₁) / ( V₂² / r₂) (rearranging & simplify)
= (V₁/V₂)² (r₂ / r₁) (substituting eq1 into equation)
= (r₁/r₂)²(r₂ / r₁) (simplifying)
= (r₁/r₂) (substituting r₁=7.17 and r₂=4.01)
= 7.17 / 4.01
= 1.789
