Question

Constants Modern wind turbines are larger than they appear, and despite their apparently lazy motion, the speed of the blades tips can be quite high-many times higher than the wind speed. A turbine has blades 58 m long that spin at 14 rpm . At the tip of a blade, what is the centripetal acceleration?

Answer 1

It is given that the length of blade of the turbine is 58 m.

During the motion, the turbine will undergo rotational motion. Hence the radius of the circle traced by the turbine is equal to the length of the blade.

Hence radius r = 58 m.

The frequency of the turbine [f] =14 rpm.

Here rpm stands for rotation per minute.

Hence the frequency of the turbine in one second-

                                                      $f=\frac{14}{60}\ s^-1$

                                                      $f=0.23333 Hz$

Here Hz[ hertz] is the unit of frequency.

The angular velocity of the turbine $\omega =2\pi f$

                                                          $\omega=2*3.14*0.2333$

                                                          $\omega=1.465124$ radian/second

Now we have to calculate the centripetal  acceleration of the blade.

Let the linear velocity of the blade is v.

we know that  linear velocity v=ωr

The centripetal acceleration is calculated as-

                                                                      $a_{c} =\frac{v^2}{r}$

                                                                            $=\frac{[\omega r]^2}{r}$

                                                                            $=\omega^2r$

                                                                            $=[1.465124]^2 *58$

                                                                            $=124.5021234 m/s^2$      [ans]