Question

You plot a θ vs time graph of a wind turbine blade and note a linear relationship. The slope of the line is 1.45 rad/s. Which of the following applies?

a. The angular acceleration is greater than 1 rad/s^2.

b. The blade is rotating at a constant angular speed.

c. The blade's kinetic energy is increasing.

d. The blade's angular speed is decreasing.

Answer 1

Given graph is between vs time and graph is linear, So

Now slope of linear graph is given by:

m = d/dt = (2 - 1)/(t2 - t1)

Now we know that angular speed is also given by:

w = d/dt, So that means slope of graph will give angular speed, and since given that graph is linear, So slope of linear graph is always constant.

m = w = d/dt = 1.45 rad/s

Which means Blade is rotating at constant angular speed.

Corect option is B.

Option A is wron, because angular acceleration, = dw/dt, since w is constant, So dw/dt = 0, which means angular acceleration is zero.

Option C is wrong, because KE = (1/2)*I*w^2, since w is constant, So KE is constant.

Option D is wrong, since slope of graph is constant, So angular speed is constant.