m,v A large commercial wind turbine has a wing span (diameter) of 110m. The inertia of this turbine has been estimated to be 2.469x107 kg•m2. On a still summer day, a big dumb Canadian goose flew into the turbine, impacting one of the blades. The goose's velocity at the moment of impact was 17.52 m/s, directed perpendicular to the blade, as in the picture to the right. The impact was at distance d=47.2 m from the center of rotation. The goose weighs 6.327 kg, and has a wing span of 1.81m. All of the goose's kinetic energy was converted into rotational energy of the turbine. If the initial angular velocity of the turbine was 0.00648 rad/s, what was the angular velocity after the impact? Include units in Sl. Positive is CW. (No Canadian goose was injured in the making of this question. Nothing happens to them. They are invincible.) Answer:
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
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