# Angular motion with constant acceleration of a ceiling fan

A ceiling fan has one red blade. Initially rotating in a counterclockwise (positive direction) with angular velocity Wo= +30 radians per second.

SEE THE ATTACHMENT FOR A PICTURE WITH KNOWN DATA.

At that instant, when the red blade makes an angle Qo= +1.4 radians from the +x axis, the current is reversed and a timer is started at 0 seconds. From that instant, the rotating fan continues through additional 60 radians while coming to a momentary stop and reversing direction, all at a constant angular acceleration.

a. Find A, the angular acceleration.

b. Develop an equation giving Q(t), the angular position as a function of time.

c. Find the angle in radians, between the plus x axis and the red blade at the

instant of the momentary stop.

d. Show a graph of Q(t) from part b.

https://brainmass.com/physics/rotation/angular-motion-constant-acceleration-ceiling-fan-5733

#### Solution Preview

a. The general equation expressing angular position Q as a function of time for any constant angular acceleration in terms of initial position Qo, initial angular velocity Wo, and angular velocity A, is:

(1) 'Q(t) = Qo + Wo t + .5 A t^2'

Similarlly, constant angular acceleration for a time interval is 'change of angular velocity divided by the time', ...

#### Solution Summary

The angular motion with constant acceleration of a ceiling fan are provided.