Answer
Each rocket should provide a steady force of 31 N.
Work Step by Step
(a) $\omega = (32~rpm)(2\pi \frac{rad}{rev})(\frac{1~m}{60~s}) = (\frac{16\pi}{15})~rad/s$
We can find the angular acceleration $\alpha$ as:
$\alpha = \frac{\omega}{t} = \frac{(\frac{16\pi}{15})~rad/s}{300~s}$
$\alpha = 0.0112~rad/s^2$
Let $m$ be the mass of a rocket and let $M$ be the mass of the cylinder. We can then find the moment of inertia of the system:
$I = \frac{1}{2}MR^2 + 4\times mr^2$
$I = \frac{1}{2}(3600~kg)(4.0~m)^2 + 4\times (250~kg)(4.0~m)^2$
$I = 44,800~kg\cdot m^2$
Next, we find the torque required to produce the acceleration.
$\tau = I \omega = (44,800~kg\cdot m^2)(0.0112~rad/s^2)$
$\tau = 502~m\cdot N$
We can use the torque to find the total required force at the edge of the cylinder.
$r\cdot F = \tau$
$F = \frac{\tau}{r} = \frac{502~m\cdot N}{4.0~m}$
$F = 125.5~N$
The total force required is 125.5 N. Since there are four rockets, each rocket should provide a force of $125.5~N/4$ which is 31 N.
