Gravitational Field of Thin Circular Disc Calculator

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Variation of Acceleration due to Gravity

✖Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it.ⓘ Mass [m]			+10% -10%
✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Theta [θ]			+10% -10%
✖Distance between centers is defined as the distance between the centers of attracting body and the body being drawn.ⓘ Distance between Centers [r_c]			+10% -10%

✖Gravitational Field at any point is equal to the negative gradient at that point.ⓘ Gravitational Field of Thin Circular Disc [I]

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Formula

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Gravitational Field of Thin Circular Disc

Formula

`"I" = -(2*"[G.]"*"m"*(1-cos("θ")))/("r"_{"c"}^2)`

Example

`"-4E^-27N/Kg"=-(2*"[G.]"*"33kg"*(1-cos("30°")))/(("3.84E^8m")^2)`

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Gravitational Field of Thin Circular Disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Gravitational Field = -(2*[G.]*Mass*(1-cos(Theta)))/(Distance between Centers^2)
I = -(2*[G.]*m*(1-cos(θ)))/(r_c^2)
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

[G.] - Gravitational constant Value Taken As 6.67408E-11

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Gravitational Field - (Measured in Newton per Kilogram) - Gravitational Field at any point is equal to the negative gradient at that point.
Mass - (Measured in Kilogram) - Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
Distance between Centers - (Measured in Meter) - Distance between centers is defined as the distance between the centers of attracting body and the body being drawn.

STEP 1: Convert Input(s) to Base Unit

Mass: 33 Kilogram --> 33 Kilogram No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Distance between Centers: 384000000 Meter --> 384000000 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = -(2*[G.]*m*(1-cos(θ)))/(r_c^2) --> -(2*[G.]*33*(1-cos(0.5235987755982)))/(384000000^2)

Evaluating ... ...

I = -4.00216833667558E-27

STEP 3: Convert Result to Output's Unit

-4.00216833667558E-27 Newton per Kilogram --> No Conversion Required

FINAL ANSWER

-4.00216833667558E-27 ≈ -4E-27 Newton per Kilogram <-- Gravitational Field

(Calculation completed in 00.020 seconds)

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Home » Physics » Gravitation » Gravitational Field » Gravitational Field of Thin Circular Disc

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< 6 Gravitational Field Calculators

Gravitational Field of Ring given Angle at any Point Outside Ring

Go Gravitational Field = -([G.]*Mass*cos(Theta))/(Distance from Center to Point^2+Radius of Ring^2)^2

Gravitational Field of Ring

Go Gravitational Field = -([G.]*Mass*Distance from Center to Point)/(Radius of Ring^2+Distance from Center to Point^2)^(3/2)

Gravitational Field of Thin Circular Disc

Go Gravitational Field = -(2*[G.]*Mass*(1-cos(Theta)))/(Distance between Centers^2)

Gravitational Field when Point is Inside of Non Conducting Solid Sphere

Go Gravitational Field = -([G.]*Mass*Distance from Center to Point)/Radius^3

Gravitational Field when Point is Outside of Non Conducting Solid Sphere

Go Gravitational Field = -([G.]*Mass)/(Distance from Center to Point^2)

Gravitational Field when Point is Outside of Conducting Solid Sphere

Go Gravitational Field = -([G.]*Mass)/Distance from Center to Point^2

Gravitational Field of Thin Circular Disc Formula

Gravitational Field = -(2*[G.]*Mass*(1-cos(Theta)))/(Distance between Centers^2)
I = -(2*[G.]*m*(1-cos(θ)))/(r_c^2)

How is gravitational field of a thin circular disc calculated?

The gravitational field of a thin circular disc is calculated by the formula E = 2GM[1-cosθ] / a² where G is the universal gravitational constant whose value is G = 6.674×10^-11 m³⋅kg^-1⋅s^-2 , M is the mass , cosθ is the angle between the line of that point to center of ring and line from that point to circumference of ring,a is the radius of the ring and r is the distance from center of ring to the point where mass is placed.

What is the unit and dimension of gravitational field of a ring?

The unit of gravitational field intensity is N/kg. The dimensional formula is given by [M⁰L¹T^-2].

How to Calculate Gravitational Field of Thin Circular Disc?

Gravitational Field of Thin Circular Disc calculator uses Gravitational Field = -(2*[G.]*Mass*(1-cos(Theta)))/(Distance between Centers^2) to calculate the Gravitational Field, Gravitational field of thin circular disc at any point is equal to the negative gradient at that point. Gravitational Field is denoted by I symbol.

How to calculate Gravitational Field of Thin Circular Disc using this online calculator? To use this online calculator for Gravitational Field of Thin Circular Disc, enter Mass (m), Theta (θ) & Distance between Centers (r_c) and hit the calculate button. Here is how the Gravitational Field of Thin Circular Disc calculation can be explained with given input values -> -4E-27 = -(2*[G.]*33*(1-cos(0.5235987755982)))/(384000000^2).

FAQ

What is Gravitational Field of Thin Circular Disc?

Gravitational field of thin circular disc at any point is equal to the negative gradient at that point and is represented as I = -(2*[G.]*m*(1-cos(θ)))/(r_c^2) or Gravitational Field = -(2*[G.]*Mass*(1-cos(Theta)))/(Distance between Centers^2). Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it, Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint & Distance between centers is defined as the distance between the centers of attracting body and the body being drawn.

How to calculate Gravitational Field of Thin Circular Disc?

Gravitational field of thin circular disc at any point is equal to the negative gradient at that point is calculated using Gravitational Field = -(2*[G.]*Mass*(1-cos(Theta)))/(Distance between Centers^2). To calculate Gravitational Field of Thin Circular Disc, you need Mass (m), Theta (θ) & Distance between Centers (r_c). With our tool, you need to enter the respective value for Mass, Theta & Distance between Centers and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Gravitational Field?

In this formula, Gravitational Field uses Mass, Theta & Distance between Centers. We can use 5 other way(s) to calculate the same, which is/are as follows -

Gravitational Field = -([G.]*Mass*Distance from Center to Point)/(Radius of Ring^2+Distance from Center to Point^2)^(3/2)
Gravitational Field = -([G.]*Mass*cos(Theta))/(Distance from Center to Point^2+Radius of Ring^2)^2
Gravitational Field = -([G.]*Mass*Distance from Center to Point)/Radius^3
Gravitational Field = -([G.]*Mass)/Distance from Center to Point^2
Gravitational Field = -([G.]*Mass)/(Distance from Center to Point^2)

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