To get a flat uniform cylindrical satellite spinning at the

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 3100 kg , a radius of 4.7 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 30 rpm in 5.5 min , starting from rest?

Solution

The angular acceleration of the satellite must be 30 rpm / 5.5 min = 5.454 rev/m² = 0.00951 rad/s²

For an angular acceleration of , T = *I where T = applied torque and I = moment of inertia of the system.

T = 4*Ft*R

The moment of inertia of the satellite is 0.5*Ms*R²
The moment of inertia of the rockets is 4*Mr*R²

4*Ft*R = (0.5*Ms*R² + 4*Mr*R²)*

Ft = *R*(Ms/8 + Mr)

Ft = 0.00951*4.7*(3100/8 + 250)

Ft = 28.49 N