Asmall fan has blades that have a radius of 0.0600 m. when the fan is turned on, the tips of the blades have a tangential acceleration of 23.7 m/s2 as the fan comes up to speed. what is the angular acceleration α of the blades?

α = 395 rad/s²

Explanation:

Main features of uniformly accelerated circular motion

A body performs a uniformly accelerated circular motion   when its trajectory is a circle and its angular acceleration is constant  (α = cte). In it the velocity vector is tangent at each point to the trajectory and, in addition, its magnitude varies uniformly.

There is tangential acceleration (at) and is constant.

at = α*R     Formula (1)

where

α  is the angular acceleration

R is the radius of the circular path

There is normal or centripetal acceleration that determines the change in direction of the velocity vector.

Data

R = 0.0600 m   :blade radius

at = 23.7 m/s² : tangential acceleration of the blades

Angular acceleration of the blades (α)

We replace data in the formula (1)

at = α*R  

23.7 = α*(0.06)

α = (23.7) / (0.06)

α = 395 rad/s²

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach