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A planetary space probe is in the shape of a cylinder. To protect it from heat on one side (from the Sun's rays), operators on the Earth put it into a "barbecue mode," that is, they set it rotating about its long axis. To do this, they fire four small rockets mounted tangentially as shown in the figure (Figure 1) (the probe is shown coming toward you). The object is to get the probe to rotate completely once every 45.0s , starting from no rotation at all. They wish to do this by firing all four rockets for a certain length of time. Each rocket can exert a thrust of 30.0N . Assume the probe is a uniform solid cylinder with a radius of 4.00m and a mass of 1500kg and neglect the mass of each rocket engine. Determine the amount of time the rockets need to be fired.
SO
We are given rotational goal (final angular velocity) . . 2pi/45s = .1396 rad/s
The initial angular velocity is 0 since it is started from rest
We are also given the Force of the rockets . . F=30N,
the mass of the space probe . . m=1500kg,
and radius . . r=4m
First we have to find the moment of Inertia (I)
I=(mr2)/2 this is for a uniform solid cylinder
I=(1500*42)/2=12,000
Then we have to find the torque (T)
T=Fr=30*4=120
The first 2 formulas are used to find the angular acceleration (a)
T=Ia
120=12000a then solve for a
.01 = a
We then use the rotational kinematic equation to find the time
w=wo+at
.1396=0+.01t
.1396=.01t
13.96=t
So the time the four rockets need to be fired is
t/4
13.96/4
3.49
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