Force Required by Rockets and Angular Acceleration

[PeachBanana]

Homework Statement

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

If the satellite has a mass of 4800 kg and a radius of 2.7m , what is the required steady force of each rocket if the satellite is to reach 29 rpm in 6.0 min?

Homework Equations

F = ma
ω final - ω initial / t = α
F/4 = force required by each rocket

The Attempt at a Solution

I converted everything to radians, seconds, etc.

I assumed the initial angular velocity was 0 rad./s.
3.0368 rad./s / 360 s. = 0.00843 rad./s^2

The rockets are being fired tangentially so I then found tangential acceleration.
(2.7 m)(0.00843 rad./s^2) = 0.022761 m/s^2

Then I used F = ma

F = (4800 kg)(0.022761 m/s^2)
F = 109.2528 N

F/4 = 27 N

 

[tms]

You are mixing translational and rotational equations here. You must stick to rotation. Instead of F = ma, you must use the rotational analog.

 

[PeachBanana]

I think I'm a tad bit closer now.

torque = moment of inertia*angular acceleration

torque = (4800 kg)*(2.7m)^2*(0.00843 rad./s^2)

torque = 294.98256 N * m

Since I want my units to contain only Newtons, shouldn't I divide by the radius?

294.98256 N * m / 2.7 m = 109.2528 N

109.2528 N / 4 = 27 N per rocket

which can't be correct because it's the same as I did before.

 

[tms]

You're using the wrong moment of inertia; the spacecraft is a cylinder, not a cylindrical shell.

 

[PeachBanana]

tms - Thank you. I obtained the correct answer of about 14 N per rocket.