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Earth rotates about itself with an angular velocity
         = ω = 2π /(86400)  rad/sec = 72.722 micro radians/sec

Radius of Earth at equator = R = 6,400 km
acceleration due to gravity = g at Equator = GMe/R² = 9.81 m/sec²

Centripetal force on a mass m on the equator = m R ω² 

Apparent weight = m g - m R ω₁²  =  0   => weightlessness

    ω₁ = √(g/R) = 1.238 milli radians/sec
    ω₁ / ω = 17.023          

SO Earth rotates about itself 17 times faster than now, then the people and objects on the Equator will feel weightlessness.