Answer:
the required revolution per hour is 28.6849
Explanation:
Given the data in the question;
we know that the expression for the linear acceleration in terms of angular velocity is;
[tex]a_{c}[/tex] = rω²
ω² = [tex]a_{c}[/tex] / r
ω = √( [tex]a_{c}[/tex] / r )
where r is the radius of the cylinder
ω is the angular velocity
given that; the centripetal acceleration equal to the acceleration of gravity a [tex]a_{c}[/tex] = g = 9.8 m/s²
so, given that, diameter = 4.86 miles = 4.86 × 1609 = 7819.74 m
Radius r = Diameter / 2 = 7819.74 m / 2 = 3909.87 m
so we substitute
ω = √( 9.8 m/s² / 3909.87 m )
ω = √0.002506477 s²
ω = 0.0500647 ≈ 0.05 rad/s
we know that; 1 rad/s = 9.5493 revolution per minute
ω = 0.05 × 9.5493 RPM
ω = 0.478082 RPM
1 rpm = 60 rph
so
ω = 0.478082 × 60
ω = 28.6849 revolutions per hour
Therefore, the required revolution per hour is 28.6849
The required revolution per hour is 28.6849
The expression for the linear acceleration with respect to the angular velocity is
= rω²
So,
ω² = / r
ω = √( / r )
Here r represent the radius of the cylinder
ω represent the angular velocity
Now
diameter = 4.86 miles = 4.86 × 1609 = 7819.74 m
And,
Radius r = Diameter / 2 = 7819.74 m / 2 = 3909.87 m
So,
ω = √( 9.8 m/s² / 3909.87 m )
ω = √0.002506477 s²
ω = 0.0500647 ≈ 0.05 rad/s
Now
1 rad/s = 9.5493 revolution per minute
So,
ω = 0.05 × 9.5493 RPM
ω = 0.478082 RPM
Now
1 rpm = 60 rph
so
ω = 0.478082 × 60
ω = 28.6849 revolutions per hour
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