Answer:
1.37 rad/s
Explanation:
Given:
Total length of the tape is, [tex]d= 297[/tex] m
Total time of run is, [tex]t = 2.1[/tex] hours
We know, 1 hour = 3600 s
So, 2.1 hours = 2.1 × 3600 = 7560 s
So, total time of run is, [tex]t= 7560[/tex] s
Inner radius is, [tex]r = 10\ mm = 0.01\ m [/tex]
Outer radius is, [tex]R = 47\ mm = 0.047\ m [/tex]
Now, linear speed of the tape is, [tex]v =\frac{d}{t}=\frac{297}{7560}=0.039\ m/s [/tex]
Let the same angular speed be [tex]\omega[/tex].
Now, average radius of the reel is given as the sum of the two radii divided by 2.
So, average radius is, [tex]R_{avg}=\frac{R+r}{2}=\frac{0.047+0.01}{2}=\frac{0.057}{2}=0.0285\ m [/tex]
Now, common angular speed is given as the ratio of linear speed and average radius of the tape. So,
[tex]\omega=\dfrac{v}{R_{avg}}\\\\\\\omega=\dfrac{0.039}{0.0285}\\\\\\\omega=1.37\ rad/s [/tex]
Therefore, the common angular speed of the reels is 1.37 rad/s.
