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A physicist will choose whatever reference frame is most convenient for the situation being analyzed. There is no problem to a physicist in including inertial forces and Newton’s second law, as usual, if that is more convenient, for example, on a merry-go-round or on a rotating planet. Noninertial (accelerated) frames of reference are used when it is useful to do so. Different frames of reference must be considered in discussing the motion of an astronaut in a spacecraft traveling at speeds near the speed of light, as you will appreciate in the study of the special theory of relativity.

Let us now take a mental ride on a merry-go-round—specifically, a rapidly rotating playground merry-go-round ( [link] ). You take the merry-go-round to be your frame of reference because you rotate together. When rotating in that noninertial frame of reference, you feel an inertial force that tends to throw you off; this is often referred to as a centrifugal force (not to be confused with centripetal force). Centrifugal force is a commonly used term, but it does not actually exist. You must hang on tightly to counteract your inertia (which people often refer to as centrifugal force). In Earth’s frame of reference, there is no force trying to throw you off; we emphasize that centrifugal force is a fiction. You must hang on to make yourself go in a circle because otherwise you would go in a straight line, right off the merry-go-round, in keeping with Newton’s first law. But the force you exert acts toward the center of the circle.

In figure a, looking down on a merry-go-round, we see a child sitting on a horse moving in counterclockwise direction with angular velocity omega. The force F sub fict is equal to the centrifugal force at the point of contact between the pole carrying horse and the merry-go-round surface. The force is radially outward from the center of the merry-go-round. This is the merry-go-round’s rotating frame of reference. In figure b, we see the situation in the inertial frame of reference.  seen rotating with angular velocity omega in the counterclockwise direction. The child on the horse is shown at the same position as in figure a. The net force is equal to the centripetal force, and points radially toward the center. In shadow, we are also shown the child as at an earlier position and at the position he would have if the net force on him were zero, which is straight forward and so at a larger radius than his actual position.
(a) A rider on a merry-go-round feels as if he is being thrown off. This inertial force is sometimes mistakenly called the centrifugal force in an effort to explain the rider’s motion in the rotating frame of reference. (b) In an inertial frame of reference and according to Newton’s laws, it is his inertia that carries him off (the unshaded rider has F net = 0 and heads in a straight line). A force, F centripetal , is needed to cause a circular path.

This inertial effect, carrying you away from the center of rotation if there is no centripetal force to cause circular motion, is put to good use in centrifuges ( [link] ). A centrifuge spins a sample very rapidly, as mentioned earlier in this chapter. Viewed from the rotating frame of reference, the inertial force throws particles outward, hastening their sedimentation. The greater the angular velocity, the greater the centrifugal force. But what really happens is that the inertia of the particles carries them along a line tangent to the circle while the test tube is forced in a circular path by a centripetal force.

Illustration of a test tube in a centrifuge, moving in a clockwise circle with angular velocity omega. The test tube is shown at two different positions: at the bottom of the circle and approximately 45 degrees later. It is oriented radially, with the open end closer to the center. The contents are at the  bottom of the test tube. The following directions are indicated: In the bottom position, the centripetal acceleration a sub c is radially inward, the velocity, v, and the inertial force are horizontally in the direction of motion (to the left in the figure.) A short time later, when the tube has moved up and to the left, the centripetal acceleration a sub c is radially inward, the inertial force is to the left, and the centrifugal force is radially outward. We are told that the particle continues to left as test tube moves up. Therefore, particle moves down in tube by virtue of its inertia.
Centrifuges use inertia to perform their task. Particles in the fluid sediment settle out because their inertia carries them away from the center of rotation. The large angular velocity of the centrifuge quickens the sedimentation. Ultimately, the particles come into contact with the test tube walls, which then supply the centripetal force needed to make them move in a circle of constant radius.

Let us now consider what happens if something moves in a rotating frame of reference. For example, what if you slide a ball directly away from the center of the merry-go-round, as shown in [link] ? The ball follows a straight path relative to Earth (assuming negligible friction) and a path curved to the right on the merry-go-round’s surface. A person standing next to the merry-go-round sees the ball moving straight and the merry-go-round rotating underneath it. In the merry-go-round’s frame of reference, we explain the apparent curve to the right by using an inertial force, called the Coriolis force    , which causes the ball to curve to the right. The Coriolis force can be used by anyone in that frame of reference to explain why objects follow curved paths and allows us to apply Newton’s laws in noninertial frames of reference.

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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