Respuesta :
Answer:
The number of revolutions is 10.68 rev/min.
Explanation:
Given that,
Radius = 8 m
Suppose, centripetal acceleration equal to the gravity
[tex]a_{c}=g=9.8[/tex]
We need to calculate the velocity
Using formula of centripetal acceleration
[tex]a_{c}=\dfrac{v^2}{r}[/tex]
[tex]v^2=a_{c}\times r[/tex]
Put the value into the formula
[tex]v=\sqrt{9.8\times8}[/tex]
[tex]v=8.85\ m/s[/tex]
We need to calculate the value of [tex]\omega[/tex]
Using formula of velocity
[tex]v=r\omega[/tex]
[tex]\omega=\dfrac{v}{r}[/tex]
Put the value into the formula
[tex]\omega=\dfrac{8.85}{8}[/tex]
[tex]\omega=1.12\rad/s[/tex]
We need to calculate the number of revolutions
Using formula of angular frequency
[tex]\omega=\dfrac{2\pi}{T}[/tex]
[tex]\omega=2\pi N[/tex]
[tex]N=\dfrac{\omega}{2\pi}[/tex]
Put the value into the formula
[tex]N=\dfrac{1.12}{2\pi}[/tex]
[tex]N=0.178\ rev/s[/tex]
Using conversion rev/s to rev/min
[tex]N=0.178\times 60[/tex]
[tex]N=10.68\ rev/min[/tex]
Hence, The number of revolutions is 10.68 rev/min.
