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How long will the rockets need to operate in order to bring the rotational velocity of the space station up from 0 rad/s to the final required value of 0.20 $\mathrm{rad} / \mathrm{s} ?$A. $2 \times 10^{4} \mathrm{s}$B. 20 $\mathrm{s}$C. 0.002 $\mathrm{s}$D. $2 \times 10^{-6} \mathrm{s}$

$2 \times 10^{4} \mathrm{s}$Therefore, the correct answer is option A

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

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Hello. We're working Problem 81 which is a multiple choice problem, and it talks about a space station. Our space station has a radius of 250 meters and it's a moment of inertia. Is 10 to the 12th kilogram meters squared? In an earlier problem we saw for the network provided by our rockets. We have 40 little rockets. Internet talk that those provide is one times 10 to the fourth Newton meters. You can see solution number 79 to get that number. Now we are told that initially our space station is at rest and we would like to reach an angular velocity point to radiance per second and question Anyone wants to know? How long is it gonna take us to do that? Well, we know from our kin O Matics formulas. If we knew our angular acceleration weakened substitute in and find the time Artur care is gonna help us find our angular acceleration. We know net torque is equal to moment of inertia times angular acceleration. We have our net torque and we know our moment of inertia was given to us solving. There we find Alfa to be one times 10 to the negative fifth radiance per second squared Subbing in up here we can find our time calculating that at a time, then becomes two times 10 to the four seconds which is option A thank you for learning with me today.

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