Final answer:
To calculate the rotation speed required to feel an effect equal to gravity at the surface of the Earth, we can use the formula for centripetal acceleration. In this case, the acceleration is equal to 0.90 times the acceleration due to gravity on Earth. To convert from revolutions per day to radians per second, we multiply by 7.28 * 10^-5 rad/s.
Step-by-step explanation:
To calculate the rotation speed required to feel an effect equal to gravity at the surface of the Earth, we can use the formula for centripetal acceleration:
a = ω^2 * r
Where a is the centripetal acceleration, ω is the angular velocity, and r is the radius from the center of rotation. In this case, the acceleration is equal to 0.90 times the acceleration due to gravity on Earth (9.80 m/s^2). We can rearrange the formula to solve for ω:
ω = sqrt(a / r) = sqrt(0.90 * 9.80 m/s^2 / r)
To convert from revolutions per day to radians per second, we multiply by 2π / (24 * 60 * 60) = 7.28 * 10^-5 rad/s:
ω = sqrt(0.90 * 9.80 m/s^2 / r) * 7.28 * 10^-5 rad/s