[5] A large lawn sprinkler with four identical arms is to be converted into a turbine to generate electric power by attaching a generator to its rotating head. Water eneters the sprinkler from the base along the axis of rotation at a rate of 20 L/s and leaves the nozzles in the tangential direction. The sprinkler rotates at a rate of 300 rpm in a horizontal plane. The diameter of each jet is 1 cm, and the normal distance between the axis of rotation and the center of each nozzle is 0.6 m. Estimate the electric power produced. (Here the power (W) can be calculated using the relation: W=wThaft That=the torque transmitted through the shaft, w-angular velocity of sprinkler)
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.
![[5] A large lawn sprinkler with four identical arms is to be converted into a turbine to
generate electric power by attaching a generator to its rotating head. Water eneters the
sprinkler from the base along the axis of rotation at a rate of 20 L/s and leaves the
nozzles in the tangential direction. The sprinkler rotates at a rate of 300 rpm in a
horizontal plane. The diameter of each jet is 1 cm, and the normal distance between
the axis of rotation and the center of each nozzle is 0.6 m. Estimate the electric power
produced. (Here the power (W) can be calculated using the relation: W=wTshaft-
Tshat =the torque transmitted through the shaft, w=angular velocity of sprinkler)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb07f71b-3a39-4ebe-a118-3d0ec49ba915%2F29778176-1042-464c-b1e0-b7f0db1bec3d%2F6ebm65v_processed.jpeg&w=3840&q=75)
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