Question

A small 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?

Answer 1

α = 395 rad/s²

Step-by-step 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