MadSci Network: Physics |
very interesting question! the first thing you have to be careful of when you are asking this question is that you should specify where the object is ( the latitude of the object). that is because the tangential velocity of an object in circular motion depends on it's distance from the axis of rotation ( the radius). at the equator, this is the greatest, while at the poles this is zero. so an object at the poles will have no tangential velocity. next we come to the question that when the earth stops rotating, why shouldn't the object stop too? well that is exactly what Newton's concept of inertia is... a body tends to MAINTAIN it's STATE OF MOTION (rest or moving) unless an external force acts on it. so if we assume that our object is unrestrained, it will keep moving even though the earth below it stops. this is also the reason why you fall forward when your car stops suddenly. the upper part of your body keeps moving while your lower part stops with the car. so now that we have established that it keeps on moving with the tangential velocity it had just before the earth stopped, let's try to analyse what kind of orbit it goes into. the reason why objects orbit the earth ( or any other heavenly body) is the gravitational attraction between the object and earth. if you leave an object without any motion in earth's gravitational field, it will fall down to earth because of the attraction. if it has a velocity pointing away from the earth's centre ( at least tangential) it will tend to go away from the earth. it is the balance of these two tendencies that determines the shape of the orbit. in other words the shape of the orbit depends on the velocity of the object. for an object to "escape" form the earth, i.e., achieve a parabolic orbit relative to the earth, a critical velocity called the escape velocity is needed. this velocity depends inversely on the distance of the object from the earth's centre ( you can get the exact formula in any physics book). from the above considerations, we might be tempted to say that the object will go into the kind of orbit dictated by it's tangential velocity. but before jumping to that conclusion, let us first consider the dynamics of the object while the earth is still rotating. to make an object execute circular motion, we need a CENTRIPETAL force. what supplies this force? gravity. but the surface of the earth exerts an oppositely directed force on the object ( the weight it feels). so the difference between the gravity force and the ground reaction must equal the centripetal force. what changes when the earth stops rotating? NOTHING ! gravity still acts, there is still ground reaction and the object still has the same tangential velocity due to inertia. so IT WILL CONTINUE to trace the SAME path in space that it was doing before...it slides on the surface of the earth ! in reality , friction will slow it down an bring it to a stop. then the ground reaction will become equal to the gravity which means that the object will become heavier.
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