part a)
The angular velocity is the ratio between the tangential velocity and the radius of the orbit:
[tex]\omega = \frac{v}{r} [/tex]
we already have the radius of the orbit, r=4.0 m, but we have to find the tangential velocity v.
We know that the perimeter of the orbit is
[tex]d=2 \pi r = 2 \pi (4.0 m)=25.12 m[/tex]
And that the Tornado takes t=2.0 s to make one revolution (so, it takes 2.0s to complete one perimeter), so the tangential velocity is
[tex]v= \frac{d}{t}= \frac{25.12 m}{2.0 s}=12.56 m/s [/tex]
Therefore, the angular velocity is
[tex]\omega= \frac{v}{r}= \frac{12.56 m/s}{4.0 m}=3.14 rad/s [/tex]
part b) The time the plane takes to do one circle is
[tex]t=35 min = 2100 s[/tex]
Similarly to what we have done before, the perimeter of the orbit is
[tex]d=2 \pi r= 2 \pi (5.0 \cdot 10^4 m)=3.14 \cdot 10^5 m[/tex]
And so the tangential velocity is
[tex]v= \frac{d}{t}= \frac{3.14 \cdot 10^5 m}{2100 s}=149.5 m/s [/tex]
And the angular velocity of the plane is given by
[tex]\omega = \frac{v}{r}= \frac{149.5 m/s}{5.0 \cdot 10^4 m}=0.003 rad/s [/tex]
