Plus, it gives physicists something to nitpick. Sometimes it is much simpler to use the accelerated reference frame, so “centrifugal force” is not really a “bad” thing. Centrifugal force is a pseudo-force used to allow us to apply Newton’s laws in an accelerated reference frame. If you try to apply Newton’s laws in this accelerated reference frame, it appears that there really is a “centrifugal” force “trying” to throw the child outward. An example of an accelerated reference frame is a child riding on a merry-go-round, from the child’s point of view. If you wish to refer your coordinates to an axis system that is accelerated, you cannot directly apply Newton’s laws. Then why do engineers (and other supposedly educated people) talk about centrifugal forces? I didn’t tell you this before, but Newton’s laws are valid only in inertial (non-accelerated) reference frames. Isn’t there an outward force, pulling the ball out? NO! What about the centrifugal force I feel when my car goes around a curve at high speed? There is no such thing as centrifugal force! But I feel a force! You feel the centripetal force of the door pushing you towards the center of the circle of the turn! Your confused brain interprets the effect of Newton’s first law as a force pushing you outward. The direction of the y-axis is irrelevant here. Choose an axis parallel to the acceleration vector. Suppose the ball (mass m) in the example I gave in the previous section moves with a constant speed V. The OSE sheet contains a variation on Newton’s second law where the subscript “r” stands for “radial.” You may also use the subscript “c” (“centripetal”). For the problems on circular motion, you need to recall the definitions of frequency, period, and know how to use the fact that that an object moving in a circle with constant speed has velocity given by v = 2r / T.ĭynamics of Uniform Circular Motion Now we consider causes (forces) of circular motion. Note: if the motion is not uniform (the speed changes or the radius of the circle changes) there will also be a tangential acceleration. If the ball moves uniformly in a circle, both the force and acceleration continually change direction, so that they always point to the center of the circle. The centripetal force due to the string gives rise to a centripetal (also called radial) acceleration. T ac The force that accelerates the ball is the tension in the string to which it is attached. If the motion is uniform circular, the acceleration is towards the center of the circle i.e., the acceleration is “radial” or “centripetal.” The ball is accelerated because its velocity constantly changes. The instantaneous acceleration is perpendicular to the velocity vector. A ball on a string: a The instantaneous velocity is tangent to the path of motion (OK to “attach” velocity to object-this is not a free-body diagram). V An object moving in a circle with constant speed is said to undergo uniform circular motion. The moon orbiting the earth (approximately). The earth orbiting the sun (approximately). A ball tied to the end of a string and “whirled” around. If you apply a force perpendicular to an object’s velocity vector, you will change its direction of motion BUT NOT ITS SPEED!Īn example of the latter is circular motion. If you apply a force parallel to the velocity vector you can only change an object’s speed, not its direction. A force applied perpendicular to an object’s velocity vector instantaneously changes the direction of the velocity vector, but not the object’s speed. Summary and consequences: A force applied parallel to an object’s velocity vector increases the object’s speed. In that case, the object follows a circular path. F Vf V=at Vi If the applied force is always perpendicular to the velocity vector, the object constantly changes direction, but never speeds up or slows down. Vi In the limit t0, the length of the velocity vector does not change.Ī force applied perpendicular to an object’s velocity vector instantaneously changes the direction of the velocity vector, but not the object’s speed. A force F applied perpendicular to the direction of motion for a time t changes the direction of the velocity vector. Vi A force applied parallel to an object’s velocity vector increases the object’s speed. Viį V=at F V=at A force F applied parallel to the direction of motion for a time t increases the magnitude of velocity by an amount at, but does not change the direction of motion. Consider an object moving in a straight line. However, let’s start by considering circular motion without looking at the forces involved. I believe our starting point for circular motion best involves forces (dynamics). Kinematics of Uniform Circular Motion Do you remember the equations of kinematics? There are analogous equations for rotational quantities.
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