The Calculus of Infintessimals (now just called "Calculus") was the first to resolve these issues consistently in a way which correlated to how you and I view reality. For thousands of years, we grappled with how to calculate with infintessimally small units Zeno's Paradox is a famous thought provoker along these lines. The handling of this sort of thinking is actually what made Newton and Libnitz's Calculus so terribly powerful. What is the "shortest interval of time?" 1 second, 1/10th of a second? 1/100th of a second? 1/100000000 of a second? In Newtonian physics, we consider an interval of time that is infinitesimally small. but in shortest interval of time the particle is just forward from its initial position. The reaction force of the arm kicks in infinitely quickly, before the particle is able to travel forward at all. But in the idealized world we use to understand physics concepts this doesn't happen. In any real experiment you are probably right: the arm (or string, or whatever attaches the "particle" to the central axis) would stretch out a little and the particle would leave the circular path after you give it a kick. So the particle doesn't end up moving forward but rather moves in a circle. it would move forward if there was no centripetal force) but the arm exerts a force toward the axis which changes the velocity of the particle. The key is that the particle "tries" to move forward (i.e. You say two things that are not necessarily consistent: first "when provided the velocity it tries to move forward" then "the particle is just forward of its initial position". At every instant the arm exerts a force toward the axis that is of exactly the right magnitude to keep the particle moving on a circle. In this case you have a perfectly rigid arm connecting the "particle" to the center point. Usually we're talking about an "idealized" experiment. The velocity changing and the force changing happens practically simultaneously over infinitesimal time intervals. we are thinking in terms of infinitesimal changes that then add up over time. You are thinking "Move forward, then force reacts later, then velocity changes later." But when we think about velocities, accelerations, etc. But more importantly, you seem to be thinking in finite, sequential steps. Won't this slows down the particle and makes it stop? But it is said it won't affect its velocity, How?Īnd now you seem to be thinking about uniform circular motion. So there is a component of force along velocity direction. This makes the angle between radius and velocity more than 90 degrees. This force is along the radius, but in shortest interval of time the particle is just forward from its initial position. This forward motion give rise to centripetel force. There has to be some force tangent to the circular path in order to speed the particle up. So we are not talking about uniform circular motion here. As soon as the particle is provided the velocity, it tries to move forward. When particle is about to start its motion there is no centripetal force. However, it is still possible in circular motion for the velocity magnitude to change if there are force components that are tangential (perpendicular to the radius). In uniform circular motion the velocity magnitude stays constant, and the net force is entirely centripetal. It looks like you are getting confused with uniform circular motion and circular motion in general. It is said that in circular motion velocity of particle is perpendicular to centripetal force, so velocity of particle won't gets affected.
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