How Fast Must Turbine Blades Spin to Store Energy?

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SUMMARY

The discussion revolves around calculating the angular velocity required for turbine blades to store 1.00 MJ of energy using a model of two steel blades, each 15.0 m long and 25.0 cm in diameter. The density of steel is specified as 7800 kg/m³. Key equations referenced include those for rotational kinetic energy and moments of inertia, which are essential for determining the necessary spin rate in both radians per second (rad/s) and revolutions per minute (rpm).

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  • Understanding of rotational kinetic energy equations
  • Familiarity with moments of inertia for cylindrical objects
  • Basic knowledge of angular velocity calculations
  • Proficiency in unit conversions between rad/s and rpm
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Angular Velocity Question?

In March 2004, a British company successfully tested a power system to tap the energy of ocean tides. The energy will be stored in an underwater turbine consisting of two metal blades, each 15.0 m long. The movement of the water due to the tides will give kinetic energy to the turbine blades, causing them to spin. In the calculations that follow, ignore any frictional drag due to the seawater.

If we model each of these two blades as a thin uniform steel bar 15.0 m long and 25.0 cm in diameter, at what rate rad/s and rpm must they spin for the turbine to store 1.00 MJ of energy? The density of steel is 7800 kg/m^3 . (Recall that density is equal to an object's mass divided by its volume.)

How do i solve this?? THANKS!
 
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