Answer:
a) [tex]r = 3.820\,m[/tex], b) [tex]v\approx 10.472\,\frac{m}{s}[/tex]
Explanation:
a) The needed length is found by the following formula:
[tex]r = \frac{v}{\omega}[/tex]
[tex]r = \frac{40\,\frac{m}{s} }{(100\,rpm)\cdot(\frac{2\cdot \pi}{1\,rev} )\cdot (\frac{1\,min}{60\,s} )}[/tex]
[tex]r \approx 3.820\,m[/tex]
b) The required speed is:
[tex]v = \omega \cdot r[/tex]
[tex]v = (100\,rpm)\cdot (\frac{2\cdot \pi}{1\,rev} )\cdot (\frac{1\,min}{60\,s} )\cdot(1\,m)[/tex]
[tex]v\approx 10.472\,\frac{m}{s}[/tex]
