Answer to Question #86988 in Mechanics | Relativity for Maria

Question

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure (Figure 1). Suppose that the satellite has a mass of 4200 kg and a radius of 4.0 m, and that the rockets each add a mass of 250 kg.
What is the steady force required of each rocket if the satellite is to reach 49 rpm in 2.5 min, starting from rest?
Express your answer to two significant figures and include the appropriate units.

Answer 1

Moment of inertia is

$$I= 0.5Mr² + 4mr² = (0.5(4200) + 4(250))(4)^2 =49600 kg·m^2$$

The angular acceleration:

$$\alpha=\frac{\omega}{t}=\frac{2\pi 49}{3600(2.5}=0.034 rad/s^2$$

The torque is

$$\tau=I\alpha=4rF$$

$$(49600)(0.034)=4(4)F$$

$$F=110 N$$