Answer in Physics for Diocos #172492

A wind turbine is rotating counterclockwise at 0.5 rev/s and slows to a stop in 10 s. Its blades are 20 m in length

1)The angular acceleration of the turbine is

2)The centripetal acceleration of the tip of the blades at t=0s is

3)The magnitude of the total linear acceleration of the tip of the blades at t=0s is

4)The direction of the total linear acceleration of the tip of the blades at t=0s is Blank ____° counterclockwise

1) We can find the angular acceleration of the turbine as follows:

“omega=omega_0+alpha t,”“alpha=dfrac{omega-omega_0}{t},”“alpha=dfrac{0-0.5 dfrac{rev}{s}cdotdfrac{2pi rad}{1 rev}}{10 s}=-0.314 dfrac{rad}{s^2}.”

The sign minus means that the turbine decelerates.

2) We can find centripetal acceleration of the tip of the blades as follows:

“a_c=omega_0^2R=(0.5 dfrac{rev}{s}cdotdfrac{2pi rad}{1 rev})^2cdot20 m=197.2 dfrac{m}{s^2}.”

3) Let’s first find the tangential acceleration of the tip of the blades:

“a_t=alpha R=(-0.314 dfrac{rad}{s^2})cdot20 m=-6.28 dfrac{m}{s^2}.”

Finally, we can find the magnitude of the total linear acceleration of the tip of the blades from the Pythagorean theorem:

“a=sqrt{a_c^2+a_t^2}=sqrt{(197.2 dfrac{m}{s^2})^2+(-6.28 dfrac{m}{s^2})^2}=197.3 dfrac{m}{s^2}.”

4) We can find the direction of the total linear acceleration of the tip of the blades from the geometry:

“tantheta=dfrac{|a_t|}{|a_c|},”“theta=tan^{-1}(dfrac{|a_t|}{|a_c|}),”“theta=tan^{-1}(dfrac{|-6.28 dfrac{m}{s^2}|}{|197.3 dfrac{m}{s^2}|})=1.82^{circ}.”