Name: earth's spin and apparent weight
Uploaded: 2023-04-30T11:06:14.000Z
Duration: 1 min 28 s
Channel: JoVE

K12 Standards

Pennsylvania State Academic Standards

9-12

Earth and Space Science

Weather and Climate

3.3.9-12.E

Apparent Weight and the Earth's Rotation

Consider an object of mass m suspended from a spring scale attached to a rigid support at the Earth&#39;s equator. The scale reading is the object&#39;s apparent weight mg&#39;, equal to the magnitude of tension force Ft in the spring.
If the Earth was a non-rotating body, the tension force would be equal to the gravitational force Fg acting on the object, keeping it in equilibrium.
Recall that the magnitude of the gravitational force is the true weight mg of the object.
However, since the Earth rotates about an axis passing through its poles, the object at the equator describes a circle around the Earth&#39;s rotational axis. Therefore, it has a centripetal acceleration directed towards the Earth&#39;s center.
Hence, the forces acting on the object are the gravitational force directed towards the Earth&#39;s center, the tension force in the spring directed away from the Earth&#39;s center, and&#160;the centripetal force directed towards the axis of rotation.
Therefore, the apparent weight equals the true weight minus the centripetal force. At the poles, the centripetal force on the object is zero, implying that mg&#39; equals mg.

apparent weight and the earth's rotation

Since all objects on the Earth&#39;s surface move through a circle every 24 hours, there must be a net centripetal force on each object, directed towards the center of that circle. The points of the north and south poles are the only exception to this rule.
For an object on the Earth&#39;s equator, the net centripetal force that accounts for its rotation is the Earth&#39;s pull towards its center, or the weight minus the normal force that prevents it from piercing into the Earth&#39;s surface. This force, called the apparent weight, is thus the object&#39;s weight minus the centripetal force.
The centripetal force is proportional to the Earth&#39;s radius and the square of the Earth&#39;s angular speed. The angular speed is relatively small; hence, the centripetal force, which is also the difference between the true and apparent weights, is itself quite small. At the equator, an object&#39;s apparent weight is only 0.34% less than its true weight, a small correction.
We can further understand this minor correction by considering how quickly the Earth would have to rotate such that all objects on the equator would feel weightless owing to the Earth&#39;s rotation. Calculations imply that the orbital period of the Earth, which is 24 hours, would have to be only 84 minutes instead.
This text is adapted from <a href="https://openstax.org/books/university-physics-volume-1/pages/13-2-gravitation-near-earths-surface">Openstax, University Physics Volume 1, Section 13.2: Gravitation Near Earth&#39;s Surface.</a>

Since all objects on the Earth&#39;s surface move through a circle every 24 hours, there must be a net centripetal force on each object, directed towards ...

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Physics

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Gravitation

KEY TERMS AND CONCEPTS

earth's spin and apparent weight

Earth’s spin changes how weight is measured on the surface. Because the Earth turns once every 24 hours, objects on the surface move in a circle. That motion requires a net centripetal force, which points toward the center of the circle. The north and south poles are the only exception.

At the equator, the force that provides this inward pull comes from Earth’s gravity. It is the difference between an object’s true weight and the normal force from the ground. The normal force is the support force that keeps an object from sinking through the surface. This difference is called the apparent weight.

The centripetal force depends on Earth’s radius and the square of its angular speed, or rotation rate. Earth’s angular speed is small, so the centripetal force is also small. At the equator, apparent weight is only 0.34% less than true weight. That makes the correction tiny in everyday life.

The size of this effect also shows why Earth does not make objects feel weightless from its rotation. For that to happen at the equator, Earth would need to spin much faster. The calculations show that the day would have to be only 84 minutes long instead of 24 hours.

Earth's Spin and Apparent Weight

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Learn how Earth’s rotation creates centripetal force, why apparent weight is slightly lower at the equator, and why the effect is very small.

Earth's Spin and Apparent Weight | JoVE K12

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3.3.9-12.S

Earth's Spin and Apparent Weight

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