A wind turbine has a radius of 37 m, a moment of inertia of 8.4 * 106kg # m2, and rotates with an initial angular speedof 1.1 rad>s. When the wind speed increases, the turbine experiences a net torque of 1.6 * 105N # m. (a) How manyrotations does it take for the angular speed to increase to 1.8 rad>s? (b) What is the linear speed of the tips of the turbineblades 27 s after the acceleration begins?
Angular speed, acceleration and displacement
Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.
Angular Position
Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.
A wind turbine has a radius of 37 m, a moment of inertia of 8.4 * 106
kg # m2
, and rotates with an initial angular speed
of 1.1 rad>s. When the wind speed increases, the turbine experiences a net torque of 1.6 * 105
N # m. (a) How many
rotations does it take for the angular speed to increase to 1.8 rad>s? (b) What is the linear speed of the tips of the turbine
blades 27 s after the acceleration begins?
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