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if the earth were to cease rotating about its axis,then what is the increase in the value of gravity?

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Newton's Universal Law of Gravitation states:\[F_g=G\frac{M_1M_2}{r^2}\]Where Fg = force of gravity, G is the gravitational constant, m1 and m2 are two masses (one of which is Earth) and r is the distance between the masses. I don't see anything about rotation in that you?
moving earth will have high mass so there is a chance for increasing gravity . because gravity is directly proportional to mass of the substance
Nothing. What you may be asking is whether there would be any change in the measured value of the acceleration due to gravity, usually given the symbol g. The answer is yes, because we normally define "the acceleration due to gravity" as that part of a body's acceleration perpendicular to the Earth's surface -- which means it does NOT include the acceleration necessary to make it go around the Earth in a curved path. If the Earth were to stop rotating, this extra bit of acceleration we "don't count" as being from gravity would be zero, so we'd probably say g had gotten bigger. Our centripetal acceleration at the equator is 4 pi^2 * R_E / day = 33.7 mm/s^2 = 0.0034 g. So if the Earth stopped rotating, and we stopped with it, presumably we'd define a value for g about 0.34% greater. Consider an extreme example: what if we were in free fall, meaning we were traveling around the Earth at the right speed to actually be in orbit, like the space station? We'd probably define a value for g of zero -- we're "weightless!" But if we now stop orbiting, and stand still, we begin to fall down, and we would now define a much larger value for g.

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If the earth were to cease rotating about its axis then the gravitational pull of the earth will dramatically increase. It is because the angular momentum conservation \[L=I*w where I is moment of inertia equals m*r^2 and w is angular velocity.\] according to this relation if earth stops rotating about its axis than its w will decrease and the I will increase and hence mass increases and thus if mass increases then the gravitational pull will increase.
Think the Earth is trying to throw you off like if you spin a wet apple on your kitchen counter. The little water droplets will fly off. Well, we are like the little water droplets and the Earth is like the apple. If the Earth stopped rotating then we would have a increase in gravitational acceleration.
There is no change in gravity, but there is a change in 'weightiness'. Gravitational force and weight relative to a frame are not the same things, although it is usually taught otherwise. Weight is actually the sum of gravitational forces and of inertial force for an object at rest (no Coriolis force) in a given frame.
If the Earth were not rotating, weight would increase most at the Equator and be unchanged at the Poles.
@rvgupta: So you're saying that when a spinning object slows down its mass must increase? I hope not :)

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