Question

When a fan is turned off, its angular speed decreases from 27 rad/s to 4.0 rad/s in 1.7 revolutions. Assuming it is constant, what is the angular acceleration of the fan?

-210 rad/s2

-1.1 rad/s2

-9.8 rad/s2

-33 rad/s2

Answer 1

Using 3rd rotational kinematic equation

w^2 = w0^2 + 2**theta

theta = angular displacement = 1.7 rev = 1.7*2*pi rad

w0 = 27 rad/sec = Initial angular speed

w = final angular speed = 4.0 rad/sec

So,

= angular acceleration = (w^2 - w0^2)/(2*theta)

= (4.0^2 - 27^2)/(2*2*pi*1.7)

= -33.3 rad/sec^2

Correct option is D.