Question

2) Many satellites use reaction wheels to change their orientation. These are small wheels inside the satellites that can turn really fast. Lets say that our particular satellite can be modeled as a rod, length L mass M, attached to a reaction wheel, radius L/10, mass M/20. If we want to give our satellite a rotational speed of ω, how fast should we turn the reaction wheel? You may use M-0.8kg, 20cm, ω = 0.02rad/s

Answer 1

moment of inerti of the rod of length 'L' I =$\frac{1}{12}ML^{2}$

angular momentum of the satellite P1= $I.\omega$

L=0.2m M= =0.8Kg, I= 0.0026; $\omega$=0.02 rad/s

Angular momentum P= 0.0026*0.02 = 5.3E-5

Moment of inertia of the wheels = I= M$R^{2}$

m= 0.04kg R=2 cm = 0.02 m; I= 1.6E-5

equating angular momentum conserved for the motion

5.3E-5 = 1.6E-5 *$\omega$1

$\omega$1= 3.3 rad/sec