Calculating Torque and Power in Flywheel Energy Storage Systems

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Flywheel energy storage systems utilize large, rotating wheels to store and quickly release energy. In this case, a flywheel with a 1.5m diameter and 270kg mass reaches a maximum angular velocity of 1200 RPM after 180 seconds, powered by a constant torque of 53 Nm. It stores 600,000 Joules of energy, with half delivered to a machine in 2.5 seconds, resulting in an average power output of 120,000 Watts. The user seeks assistance in calculating the torque exerted by the flywheel on the machine, having attempted to use energy and power equations but arriving at an incorrect answer. Clarification on the correct approach to find the torque is requested.
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Homework Statement


Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5m diameter and a mass of 270kg . Its maximum angular velocity is 1200rmp .


a)A motor spins up the flywheel with a constant torque of 53Nm . How long does it take the flywheel to reach top speed?
Ans:180s

b) How much energy is stored in the flywheel?
Ans:6*10^5 J

c) The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.5s . What is the average power delivered to the machine?

Ans:120000Watt

MY QUESTION IS:
d)How much torque does the flywheel exert on the machine?

Homework Equations


k=0.5*Iw^2
torque=F*r=Ialpha
P=F*v


The Attempt at a Solution



I try to solve with 2.5x120000= 0.5*Iw^2 then use w to find alpha and finally solve for the
Torque, but my answer is wrong... Can anyone gve me a hint??
 
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