: Rotational Equilibrium and Rotational Dynamics

Question

You turned on your classroom ceiling fan at its lowest setting. You measured that the rotation is 250 rev/min. When adjusted to its maximum setting, the speed increases to 450 rev/min in 15 s. (a) What is the angular acceleration of the blades? (b) How many revolutions do the blades go through while accelerating? USE THE GUESS METHOD.

Answer 1

The initial speed (w0 - read "omega zero" ) is 250 rev / minute. The final speed (w1) is 450 rev / minute. The constant acceleration of 200 rev / min is over 15 seconds, or 1/4 minute. Thus, over a full minute, the acceleration would be 800 rev / min, and so the rate of acceleration is alpha = 800 rev / min^2.

For the total angle covered, we integrate:

delta theta = integral of w(t) from t=0 to t=1/4

delta theta = integral of 250 + 800t from t=0 to t=1/4

delta theta = 62.5 + (1/2) * 800 * (1/4)^2

delta theta = 87.5 rev