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

Considere um objeto de massa m suspenso por uma escala de mola presa a um suporte rígido no equador da Terra. A leitura da escala é o peso aparente do objeto mg', igual à magnitude da força de tensão Ft na mola.
Se a Terra fosse um corpo não rotativo, a força de tensão seria igual à força gravitacional Fg atuando sobre o objeto, mantendo-o em equilíbrio.
Lembre-se de que a magnitude da força gravitacional é o peso real mg do objeto.
No entanto, como a Terra gira em torno de um eixo que passa por seus pólos, o objeto no equador descreve um círculo em torno do eixo de rotação da Terra. Portanto, tem uma aceleração centrípeta direcionada para o centro da Terra.
Portanto, as forças que atuam sobre o objeto são a força gravitacional direcionada para o centro da Terra, a força de tensão na mola direcionada para longe do centro da Terra e a força centrípeta direcionada para o eixo de rotação.
Portanto, o peso aparente é igual ao peso real menos a força centrípeta. Nos pólos, a força centrípeta sobre o objeto é zero, o que implica que mg' é igual a mg.

peso aparente e a rotação da terra

Uma vez que todos os objetos na superfície da Terra se movem em um círculo a cada 24 horas, deve haver uma força centrípeta resultante em cada objeto, direcionada para o centro desse círculo. Os pontos dos polos norte e sul são a única exceção a essa regra.

Para um objeto na linha do Equador da Terra, a força centrípeta resultante que explica sua rotação é a atração da Terra em direção ao seu centro, ou seja, o peso menos a força normal que o impede de perfurar a superfície da Terra. Essa força, chamada de peso aparente, é então o peso do objeto menos a força centrípeta.

A força centrípeta é proporcional ao raio da Terra e ao quadrado da velocidade angular da Terra. A velocidade angular é relativamente pequena; portanto, a força centrípeta, que também é a diferença entre os pesos verdadeiro e aparente, é bastante pequena. No equador, o peso aparente de um objeto é apenas 0,34% menor que seu peso verdadeiro, o que é apenas uma pequena correção.

Podemos entender ainda mais essa correção menor considerando o quão rapidamente a Terra teria que girar para que todos os objetos no equador se sentissem sem peso devido à rotação da Terra. Cálculos indicam que o período orbital da Terra, que é de 24 horas, teria que ser de apenas 84 minutos.

Este texto foi adaptado de <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's Surface.</a>

Peso aparente e a rotação da Terra

Uma vez que todos os objetos na superfície da Terra se movem através de um círculo a cada 24 horas, deve haver uma força centrípeta líquida em cada objeto, direcionada para ...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Gravitation

Gravitação

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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

gravitation

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reduced mass coordinates: isolated two-body problem

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acceleration due to gravity on earth

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acceleration due to gravity on other planets

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Measuring Gravity on Distant Planets

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How Earth’s Shape Affects Apparent Weight

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escape velocity

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circular orbits and critical velocity for satellites

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Orbital Speed and Period in Circular Paths

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energy of a satellite in a circular orbit

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Satellite Orbits and Energy in Space

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kepler's first law of planetary motion

Planet Orbits as Ellipses

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kepler's second law of planetary motion

Kepler's Equal-Area Planet Motion

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kepler's third law of planetary motion

Kepler’s Planet Distance Law

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tidal forces

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schwarzschild radius and event horizon

Escape Velocity Limits and Black Holes

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space-time curvature and the general theory of relativity

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Einstein’s Gravity and Mercury’s Orbit

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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 - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

Louisiana Student Standards for Science

High School

Earth Science

Earth’s Systems

HS-ESS2-4

ohios-learning-standards-and-model-curriculum

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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