How much tangential force will be needed to stop the earth in one year, if it is rotating with an angular velocity of `7.3 xx 10^(-5) rad//s` ? Given moment of inertia of earth `= 9.3 xx 10^(37) kg m^(2)` and radius of earth `= 6.4 xx 10^(6) m`.

Explanation

`F = ? omega_(2) = 0, t = 1 year = 365 xx 24 xx 60 xx 60 s`
`omega_(1) = 7.3 xx 10^(-5) rad//s, I = 9.3 xx 10^(37) kg m^(2)`
`R = 6.4 xx 10^(6) m`
From `omega_(2) - omega_(1) = alpha t`
`alpha = (omega_(2) - omega_(1))/(t) = (0 - 7.3 xx10^(-5))/(365 xx 24 xx 60 xx 60) rad//s^(2)`
`tau = I alpha = 9.3 xx 10^(37) ((7.3 xx 10^(-5))/(365xx24 xx 60 xx 60))`
`= (9.3 xx 7.3)/(365 xx 24 xx 36) xx 10^(30)N-m`
As `tau = F xx r :. F = (tau)/(r )`
`F = (9.3 xx 7.3 xx 10^(30))/(365 xx 24 xx 36) xx (1)/(6.4 xx 10^(6))`
`F = 3.364 xx 10^(19) N`