Question

During a gust of wind, the blades of the windmill are given an angular acceleration of α=(0.2 θ) rad/s2, where θ is measured in radians. If initially the blades have an angular velocity of 5 rad/s, determine the speed of point P located at the tip of one of the blades just after the blade has turned two revolutions.

Answer 1

Answer:

7.5 rad/s

Explanation:

$\alpha$ = angular acceleration = (0.2) θ

Angular acceleration is given as

$\alpha =\frac{dw}{dt}$

$\alpha =\frac{dw}{d\theta }\frac{d\theta }{dt}$

$\alpha d\theta = w{dw}$

$(0.2)\theta  d\theta = w{dw}$

Integrating both side

$(0.2)\int_{0}^{4\pi }\theta  d\theta = \int_{5}^{w}w{dw}$

$15.8 = \frac{w^{2} - 25}{2}$

w = 7.5 rad/s