Question

^{Patrons on an amusement park ride called the Rotor stand with their backs against the wall of a rotating cylinder while the floor drops away beneath them. To keep from sliding downward, they require a centripetal acceleration in excess of about 25 ms^-2. The rotor has a diameter of 5.0 m. What is the minimum frequency for its rotation?}

Answer 1

Solution.

$a=25 m/s^2;$

$d=5m;$

$n -?;$

$a=\dfrac{v^2}{r}\implies v=\sqrt{ar};$

$v=\sqrt{25\sdot2.5}=\sqrt{62.5}=7.9 m/s;$

$v=2\pi rn\implies n=\dfrac{v}{2\pi r};$

$n=\dfrac{7.9}{2\sdot 3.14\sdot2.5}=0.5s^{-1};$