## Homework Statement

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure.

If the satellite has a mass of 3700 kg, a radius of 5.0 m, and the rockets each add a mass of 250 kg, what is the required steady force of each rocket if the satellite is to reach 33 rpm in 5.5 min, starting from rest?

can anyone help me to solve this problem?

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Hootenanny
Staff Emeritus
Gold Member
Welcome to PF caner cem,

The forum guidelines require you to show some effort or detail your thoughts before we can help you. So, what have you tried thus far?

sorry, i am in a hurry.

i found the inertia of satellite I =0.5mr^2 and angular accelaration with this w = at = 33 rpm = 33*2*pi/60 = 3.455 rad/s. then calculate the torque
Torque = I*a with this equation after that i divided it 4 to find each rocket torque.
Torque = Frsin(angle between F,r) = Fr i used this equation to find the F but i could not find the right answer i am doing something wrong.

Hootenanny
Staff Emeritus
Gold Member
How did you calculate the angular acceleration?

What value did you get for the inertia?

Inertia=46250 , angular acceleration=0.0105, torque=485.63 and each torque of rocket=121.4 finally F=24.3 but it says it is wrong

i think the problem is accelaration but i do not know another solution.
i used this equation w=a.t, w: angular velocity, a:angular accelaration, t is time

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Hootenanny
Staff Emeritus
Gold Member
Inertia=46250 , angular acceleration=0.0105, torque=485.63 and each torque of rocket=121.4 finally F=24.3 but it says it is wrong

i think the problem is accelaration but i do not know another solution.
i used this equation w=a.t, w: angular velocity, a:angular accelaration, t is time
Your forgetting the moment of inertia of the rockets.

Your forgetting the moment of inertia of the rockets.

i tried to do adding the inertias of rockets but it did not accept it and i have only one time to write the answer

Hootenanny
Staff Emeritus
Gold Member
i tried to do adding the inertias of rockets but it did not accept it and i have only one time to write the answer
You need to calculate the inertia of the cylinder and rockets as a single body and use this inertia to calculate the net torque. You can treat the rockets as point masses.

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You need to calculate the inertia of the cylinder and rockets as a single body and use this inertia to calculate the angular acceleration. You can treat the rockets as point masses.

sorry. how can i find the angular accelaration using inertia?

Hootenanny
Staff Emeritus
Gold Member
sorry. how can i find the angular accelaration using inertia?
Sorry, it was a typo, I meant net torque as opposed to angular acceleration. I have corrected the mistake in my previous post.

i tried it; when i calculate the inertia with rockets I=58750 and a=0.0105 so net torque=616.875, each rocket needs to provide a torque of 616.875/4=154.22 so F=30.84 but i is wrong:(:(

Hootenanny
Staff Emeritus
Gold Member
i tried it; when i calculate the inertia with rockets I=58750
You have calculated the moment of inertia incorrectly. What is the moment of inertia for a point particle?

You have calculated the moment of inertia incorrectly. What is the moment of inertia for a point particle?
then i must use this equation with total mass I =mr^2, is it right?

Hootenanny
Staff Emeritus
Gold Member
then i must use this equation with total mass I =mr^2, is it right?
That is correct, this will give you the moment of inertia of the rockets. You then need to add this to the moment of inertia of your cylinder to obtain the total moment of inertia.

That is correct, this will give you the moment of inertia of the rockets. You then need to add this to the moment of inertia of your cylinder to obtain the total moment of inertia.

thank you very much brother. and i am so sorry to take your time.

Hootenanny
Staff Emeritus
No worries, that's what we're here for! No apology necessary 