Calculating Torque and Power in Flywheel Energy Storage Systems

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SUMMARY

This discussion focuses on calculating torque and power in flywheel energy storage systems, specifically using an industrial flywheel with a diameter of 1.5m and a mass of 270kg. The flywheel reaches a maximum angular velocity of 1200 RPM with a constant torque of 53 Nm, taking 180 seconds to reach top speed. The energy stored in the flywheel is calculated to be 600,000 J, and when half of this energy is delivered to a machine in 2.5 seconds, the average power output is 120,000 Watts. The user seeks assistance in determining the torque exerted by the flywheel on the machine.

PREREQUISITES
  • Understanding of rotational dynamics and angular velocity
  • Familiarity with the equations of motion for rotational systems
  • Knowledge of energy storage principles in mechanical systems
  • Basic proficiency in calculating power and torque
NEXT STEPS
  • Study the relationship between torque and angular acceleration using the equation torque = I * alpha
  • Explore the concept of kinetic energy in rotational systems, specifically k = 0.5 * I * w^2
  • Learn how to calculate average power delivered in mechanical systems
  • Investigate the effects of varying torque on flywheel performance in energy storage applications
USEFUL FOR

Mechanical engineers, energy storage system designers, and students studying rotational dynamics will benefit from this discussion, particularly those focused on flywheel technology and energy efficiency in mechanical systems.

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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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