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

Stellen Sie sich ein Objekt mit der Masse m vor, das an einer Federwaage hängt, die an einer starren Stütze am Äquator der Erde befestigt ist. Der Messwert der Skala ist das scheinbare Gewicht mg' des Objekts, das der Größe der Zugkraft Ft in der Feder entspricht.
Wenn die Erde ein nicht rotierender Körper wäre, wäre die Spannungskraft gleich der Gravitationskraft Fg, die auf das Objekt wirkt und es im Gleichgewicht hält.
Erinnern wir uns daran, dass die Größe der Gravitationskraft das wahre Gewicht mg des Objekts ist.
Da sich die Erde jedoch um eine Achse dreht, die durch ihre Pole verläuft, beschreibt das Objekt am Äquator einen Kreis um die Rotationsachse der Erde. Daher hat er eine Zentripetalbeschleunigung, die auf den Erdmittelpunkt gerichtet ist.
Die Kräfte, die auf das Objekt wirken, sind also die Gravitationskraft, die auf den Erdmittelpunkt gerichtet ist, die Zugkraft in der Feder, die vom Erdmittelpunkt weg gerichtet ist, und die Zentripetalkraft, die auf die Rotationsachse gerichtet ist.
Das scheinbare Gewicht ist also gleich dem wahren Gewicht abzüglich der Zentripetalkraft. An den Polen ist die Zentripetalkraft auf das Objekt Null, was bedeutet, dass mg' gleich mg ist.

scheinbares gewicht und die erdrotation

Da sich alle Objekte auf der Oberfläche der Erde alle 24 Stunden in einem Kreis bewegen, muss es eine auf jedes Objekt wirkende netto Zentripetalkraft geben, die zum Zentrum dieses Kreises gerichtet ist. Die Punkte der Nord- und Südpole sind die einzige Ausnahme von dieser Regel.

Für ein Objekt am Äquator der Erde ist die netto Zentripetalkraft, die seine Rotation erklärt, die Zugkraft der Erde zum Zentrum hin oder die Gewichtskraft minus die Normalkraft, die verhindert, dass es in die Erdoberfläche eindringt. Diese Kraft, als Scheinbares Gewicht bezeichnet, ist daher das Gewicht des Objekts minus die Zentripetalkraft.

Die Zentripetalkraft ist proportional zum Radius der Erde und dem Quadrat der Winkelgeschwindigkeit der Erde. Die Winkelgeschwindigkeit ist relativ gering, daher ist auch die Zentripetalkraft, die auch der Unterschied zwischen dem wahren und dem scheinbaren Gewicht ist an sich ziemlich gering. Am Äquator beträgt das scheinbare Gewicht eines Objekts nur 0,34% weniger als sein wahres Gewicht, eine kleine Korrektur.

Wir können diese geringfügige Korrektur weiter verstehen, indem wir uns überlegen, wie schnell sich die Erde drehen müsste, damit sich alle Objekte am Äquator gewichtslos anfühlen würden aufgrund der Rotation der Erde. Berechnungen lassen darauf schließen, dass die Umlaufzeit der Erde, die normalerweise 24 Stunden beträgt, stattdessen nur 84 Minuten betragen müsste.

Dieser Text ist angepasst von <a href="https://openstax.org/books/university-physics-volume-1/pages/13-2-gravitation-near-earths-surface">Openstax, University Physics Volume 1, Abschnitt 13.2: Gravitation nahe der Erdoberfläche.</a>

Scheinbares Gewicht und die Erdrotation

Da sich alle Objekte auf der Erdoberfläche alle 24 Stunden durch einen Kreis bewegen, muss auf jedem Objekt eine Nettozentripetalkraft wirken, die auf ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Gravitation

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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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key terms and concepts

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

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Louisiana Student Standards for Science

High School

Earth Science

Earth’s Systems

HS-ESS2-4

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Ohio’s Learning Standards and Model Curriculum

Forces, Momentum And Motion

Gravitational force and fields

Virginia  Standards of Learning

HIgh School

ES.3

ES.3.b

PH.3

PH.3.b

Florida Department of Education

SC.912.E.5

SC.912.E.5.10

SC.912.E.5.11

Texas Essential Knowledge and Skills

PHYS.5

PHYS.5.H

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

Earth and Space Science (ESS)

Earth’s Place in the Universe

E-ESS1-6.

new-york-state-science-learning-standards

New York State Science Learning Standards

Physical Science

HS. Forces and Interactions

HS-PS2-4.

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3.3.9-12.S

Earth's Spin and Apparent Weight

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