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To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rock
If the satellite has a mass of 3700 , a radius of 4.6 , and the rockets each add a mass of 240 , what is the required steady force of each rocket if the satellite is to reach 30 in 5.1 , starting from rest?
Equations for angular acceleration and change in angular velocity:
Δω = αΔt
α = τ/I
Combine them
Δω = (τ/I)Δt
We know Δω, I, Δt and part of τ.
Δω is 30
Δt is 5.1
I = I(cylinder) = ½mr^2 = 0.5×3700×(4.6^2) = 39146
τ = rF = 4.6×F, and we are looking for F
Plug everything in
Δω = (τ/I)Δt
30 = [(4.6×F)/(39146)]5.1
F = 50058.82
EDIT: Oops! I forgot about the _four_ rockets and their masses. Redo the calculations with
I = I(cylinder) + 4×240×4.6^2
Then divide the final force by 4.
!
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