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An illustration of an airplane coming toward us and banked (that is, tilted) by an angle theta in the clockwise direction, again as viewed by us. The weight w is shown as an arrow pointing straight down. A force L is shown pointing perpendicular to the wings, at an angle theta to the right of vertically up. The horizontal component of the force L is shown pointing to the right and is labeled as vector L sub horizontal. Dashed lines complete the parallelogram defined by vectors L and w, and show that the vertical component of L is the same size as w.
In a banked turn, the horizontal component of lift is unbalanced and accelerates the plane. The normal component of lift balances the plane’s weight. The banking angle is given by θ . Compare the vector diagram with that shown in [link] .

Join the ladybug in an exploration of rotational motion. Rotate the merry-go-round to change its angle or choose a constant angular velocity or angular acceleration. Explore how circular motion relates to the bug’s xy -position, velocity, and acceleration using vectors or graphs.

A circular motion requires a force, the so-called centripetal force, which is directed to the axis of rotation. This simplified model of a carousel demonstrates this force.

Inertial forces and noninertial (accelerated) frames: the coriolis force

What do taking off in a jet airplane, turning a corner in a car, riding a merry-go-round, and the circular motion of a tropical cyclone have in common? Each exhibits inertial forces—forces that merely seem to arise from motion, because the observer’s frame of reference is accelerating or rotating. When taking off in a jet, most people would agree it feels as if you are being pushed back into the seat as the airplane accelerates down the runway. Yet a physicist would say that you tend to remain stationary while the seat pushes forward on you. An even more common experience occurs when you make a tight curve in your car—say, to the right ( [link] ). You feel as if you are thrown (that is, forced ) toward the left relative to the car. Again, a physicist would say that you are going in a straight line (recall Newton’s first law) but the car moves to the right, not that you are experiencing a force from the left.

Figure a is an illustration of a driver steering a car to the right, as viewed from above. A fictitious force vector F sub fict pointing to the left is shown acting on her. In figure b, the same car and driver are illustrated but the actual force vector, F sub actual,  acting on the driver is shown pointing to the right. In figure b, the driver is shown tilting to the left.
(a) The car driver feels herself forced to the left relative to the car when she makes a right turn. This is an inertial force arising from the use of the car as a frame of reference. (b) In Earth’s frame of reference, the driver moves in a straight line, obeying Newton’s first law, and the car moves to the right. There is no force to the left on the driver relative to Earth. Instead, there is a force to the right on the car to make it turn.

We can reconcile these points of view by examining the frames of reference used. Let us concentrate on people in a car. Passengers instinctively use the car as a frame of reference, whereas a physicist might use Earth. The physicist might make this choice because Earth is nearly an inertial frame of reference, in which all forces have an identifiable physical origin. In such a frame of reference, Newton’s laws of motion take the form given in Newton’s Laws of Motion . The car is a noninertial frame of reference    because it is accelerated to the side. The force to the left sensed by car passengers is an inertial force    having no physical origin (it is due purely to the inertia of the passenger, not to some physical cause such as tension, friction, or gravitation). The car, as well as the driver, is actually accelerating to the right. This inertial force is said to be an inertial force because it does not have a physical origin, such as gravity.

Practice Key Terms 6

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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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