A Windmill's Angular Velocity Calculation

A windmill for generating electricity has a blade that is 30 feet long. Depending on the wind, it rotates at various velocities

What is the angular velocity in rad/sec for the tip of the blade if the windmill is rotating at a rate of 80 rev/sec?

A) 502.7 rad/sec
B) 502.4 rad/sec
C) 502.8 rad/sec
D) 502.6 rad/sec

Final answer:

The angular velocity in rad/sec for the tip of the blade is approximately 502.6 rad/sec.

Explanation:

To find the angular velocity in rad/sec for the tip of the blade, we need to first convert the given rotation rate from rev/sec to rad/sec. One revolution is equal to 2π radians, so the given rate of 80 rev/sec can be converted to 80 x 2π rad/sec.

Next, we need to find the circumference of the circle that the tip of the blade traces. The circumference is given by 2πr, where r is the length of the blade.

Therefore, the angular velocity in rad/sec is equal to the rotation rate multiplied by the circumference, so it is 80 x 2π x 30 = 1508π rad/sec. Rounded to the nearest tenth, this is approximately 502.6 rad/sec.