Rotational Position & Displacement Video Lessons

Concept

# Problem: Two wind turbines are set up with the following conditions:Turbine A has blades that are twice as long as the blades on Turbine B. The tips of the blades on Turbine A are moving twice as fast as the tips of the blades on Turbine B.Part AWhich turbine takes the lesser amount of time to rotate through 1.0 radian of angular displacement?a. turbine Ab. They take the same amount of time.c. turbine Bd.The answer cannot be determined from the information given.Part BAs in Part A, two wind turbines with different length blades are rotating. Consider what needs to happen in order to change the angular speed of one of the turbines. If the turbine is to spin more quickly, should the angular acceleration,  be positive or negative?a. α⃗  should be negative.b. α⃗  should be positive.c. We cannot tell which direction α⃗  should be without knowing the direction of the angular velocity, ω

###### FREE Expert Solution

Angular velocity:

$\overline{){\mathbf{\omega }}{\mathbf{=}}\frac{\mathbf{∆}\mathbf{\theta }}{\mathbf{∆}\mathbf{t}}}$

Where Δθ is angular displacement and ω is angular velocity

Linear velocity:

$\overline{){\mathbf{v}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\omega }}}$

ra = 2rb

va = 2vb

Part A

t = Δθ/ω

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###### Problem Details

Two wind turbines are set up with the following conditions:

Turbine A has blades that are twice as long as the blades on Turbine B. The tips of the blades on Turbine A are moving twice as fast as the tips of the blades on Turbine B.

Part A

Which turbine takes the lesser amount of time to rotate through 1.0 radian of angular displacement?

a. turbine A

b. They take the same amount of time.

c. turbine B

d.The answer cannot be determined from the information given.

Part B

As in Part A, two wind turbines with different length blades are rotating. Consider what needs to happen in order to change the angular speed of one of the turbines. If the turbine is to spin more quickly, should the angular acceleration,  be positive or negative?

a. α⃗  should be negative.

b. α⃗  should be positive.

c. We cannot tell which direction α⃗  should be without knowing the direction of the angular velocity, ω