Let us imagine a satellite with two flywheels spinning at a constant speed in opposite directions attached to a motor/ge

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Let Us Imagine A Satellite With Two Flywheels Spinning At A Constant Speed In Opposite Directions Attached To A Motor Ge 1 (372.15 KiB) Viewed 33 times

Let us imagine a satellite with two flywheels spinning at a constant speed in opposite directions attached to a motor/generator set. This allows them to send energy from one to the other to speed up one flywheel and slow down the other, we can assume no loss of transmissible energy between the wheels between the M/G drive. We can also make a few more assumptions: 1. The satellite is not acted upon by external forces. 2. The satellite's only motion is on the Z-axis. 3. The satellite has a mass m, which can be lumped into three identical points m5, m6, & m7 separated at equal angels at a distance of Rs. 4. The Z-axis of the flywheel arrangements is shared with the satellite. The satellite has an initial angular speed of wo at am initial time to. If each flywheel has a mass of m, that can be expressed as an equivalent masses that rotate together for each flywheel (i.e. m₁₁-m₁ & m₂ and mf1= m3 & m₁ at a distance of R₁) find the rotational speed of the two flywheels to slow the sphere down to one-half of wo if only energy can move from one wheel to the other. Part A (1 pt) Write a kinematic equation for the conservation of energy for the system (express in final terms of the mass of the sphere and flywheel. Since the flywheels are being used to store energy they will have an initial angular velocity in the equation that will need to be considered. Their initial angular velocity is also part of the resistance to change attitude. Make sure to substitute in the target velocity's behavior with the original velocity. Part B (1 pt) Solve the equation from part A where all of the variable about the change of the flywheel speeds are on the left side of the equal sign. Part C (1 pt) Set up a conservation of energy for the two flywheels for before and after the attitude change. Solve the balance for one of the flywheel angular velocities. This equation will be expressed as four different angular velocities (the two flywheels before and after the attitude adjustment). Bonus (3pt) Solve for the amount of energy from one flywheel to the other (the delta stored energy). This would be the amount of energy needed to be present in the wheels in order for this correction to be executed.