You weigh yourself on a scale inside an airplane flying due...

Name: Problem 63, Chapter 12: Physics
Uploaded: 2020-04-01T23:28:30-08:00
Duration: 2 min 2 s
Channel: Andy Chen
Description: You weigh yourself on a scale inside an airplane flying due east above the equator. If the airplane now turns around and heads due west with the same speed, will the reading on the scale increase, decrease, or stay the same? Explain.

You weigh yourself on a scale inside an airplane flying due east above the equator. If the airplane now turns around and heads due west with the same speed, will the reading on the scale increase, decrease, or stay the same? Explain.

Key Concepts

Apparent Weight

Apparent weight is the normal force exerted on an object as measured by a scale, which may differ from the gravitational force due to the presence of additional accelerations or fictitious forces. In situations where an object is moving relative to a rotating system like Earth, the apparent weight reflects not just gravitational pull but also adjustments for extra centrifugal effects resulting from that motion.

Relative Velocity in Rotational Motion

Relative velocity in a rotating system is critical because an object’s speed relative to the rotation axis determines the strength of the centrifugal force experienced. If an object moves in the same direction as the rotation, its speed relative to the axis increases, enhancing the centrifugal effect and reducing apparent weight; if it moves in the opposite direction, the effect is diminished, thereby increasing the apparent weight.

Centrifugal Force

In a rotating frame, such as that of Earth, centrifugal force is a fictitious force that appears to push objects outward from the axis of rotation. It depends on the square of the effective rotational speed. When an object moves in the same or opposite direction as the Earth's rotation, its speed relative to the center of rotation changes, thus altering the magnitude of the centrifugal force acting on it, which in turn changes its apparent weight.

Rotating Reference Frames

A rotating reference frame is a non-inertial frame of reference in which fictitious forces, such as centrifugal and Coriolis forces, appear due to the acceleration of the frame itself. Understanding motion and force measurements in these frames requires accounting for these additional forces, which can modify how weight is perceived or measured.

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