Answer:
0.114 rad/s
Explanation:
As the plastic tape is coming off from 1 reel onto another reel, the velocity of the 2 reels must be the same. For the angular speed to be the same, their radius must be the same as well since:
[tex]v = \omega * r[/tex]
Let this radius be r, we know that 12 < r < 36 mm and r is somewhere so that the area of the donut-shaped object between 12mm and r is the same as the area of the donut-shaped object between r and 36mm
In math terms:
[tex]\pi r^2 – \pi 12^2 = \pi 36^2 – \pi r^2 [/tex]
From here we can divide both sides by π
[tex]r^2 - 144 = 1296 - r^2[/tex]
[tex]2r^2 = 1440[/tex]
[tex]r^2 = 720[/tex]
[tex]r = \sqrt{720} = 26.8mm[/tex] or 0.0268m
1.7 hours = 1.7*3600 = 6120 seconds
The velocity of the tapes is 187 / 6120 = 0.031 m/s
And so the angular speed at radius r = 0.0268m is
[tex]\omega = \frac{v}{r} = \frac{0.031}{0.0268} = 0.114 rad/s [/tex]
