Radius 1 of Rotation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radius 1 of Rotation = Mass 2*Radius of Mass 2/Mass 1
Rr1 = m2*R2/m1
This formula uses 4 Variables
Variables Used
Radius 1 of Rotation - (Measured in Meter) - Radius 1 of Rotation is a distance of mass 1 from the center of mass.
Mass 2 - (Measured in Kilogram) - Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it.
Radius of Mass 2 - (Measured in Meter) - Radius of Mass 2 is a distance of mass 2 from the center of mass.
Mass 1 - (Measured in Kilogram) - Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it.
STEP 1: Convert Input(s) to Base Unit
Mass 2: 16 Kilogram --> 16 Kilogram No Conversion Required
Radius of Mass 2: 3 Centimeter --> 0.03 Meter (Check conversion here)
Mass 1: 14 Kilogram --> 14 Kilogram No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Rr1 = m2*R2/m1 --> 16*0.03/14
Evaluating ... ...
Rr1 = 0.0342857142857143
STEP 3: Convert Result to Output's Unit
0.0342857142857143 Meter -->3.42857142857143 Centimeter (Check conversion here)
FINAL ANSWER
3.42857142857143 โ‰ˆ 3.428571 Centimeter <-- Radius 1 of Rotation
(Calculation completed in 00.004 seconds)

Credits

Created by Nishant Sihag
Indian Institute of Technology (IIT), Delhi
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Verified by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
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13 Reduced Mass and Radius of Diatomic Molecule Calculators

Radius 2 given Moment of Inertia
Go Radius 2 given Moment of Inertia = sqrt((Moment of Inertia-(Mass 1*Radius of Mass 1^2))/Mass 2)
Radius 1 given Moment of Inertia
Go Mass 2 of Diatomic Molecule = sqrt((Moment of Inertia-(Mass 2*Radius of Mass 2^2))/Mass 1)
Mass 2 given Moment of Inertia
Go Mass 2 given Moment of Inertia = (Moment of Inertia-(Mass 1*Radius of Mass 1^2))/Radius of Mass 2^2
Mass 1 given Moment of Inertia
Go Mass2 of object1 = (Moment of Inertia-(Mass 2*Radius of Mass 2^2))/Radius of Mass 1^2
Radius 1 given Rotational Frequency
Go Mass 2 of Diatomic Molecule = Velocity of Particle with Mass m1/(2*pi*Rotational Frequency)
Radius 1 of Rotation given Masses and Bond Length
Go Radius 1 of Rotation = Mass 2*Bond Length/(Mass 1+Mass 2)
Radius 2 of Rotation given Masses and Bond Length
Go Radius of Mass 2 = Mass 1*Bond Length/(Mass 1+Mass 2)
Radius 2 given Rotational Frequency
Go Radius of Mass 2 = Velocity of Particle with Mass m2/(2*pi*Rotational Frequency)
Reduced Mass
Go Reduced Mass = ((Mass 1*Mass 2)/(Mass 1+Mass 2))
Mass 1 of Diatomic Molecule
Go Mass 1 of Diatomic Molecule = Mass 2*Radius of Mass 2/Radius of Mass 1
Mass 2 of Diatomic Molecule
Go Mass 2 of Diatomic Molecule = Mass 1*Radius of Mass 1/Radius of Mass 2
Radius 2 of Rotation
Go Radius 1 given Rotational Frequency = Mass 1*Radius of Mass 1/Mass 2
Radius 1 of Rotation
Go Radius 1 of Rotation = Mass 2*Radius of Mass 2/Mass 1

13 Reduced Mass and Radius of Diatomic Molecule Calculators

Radius 2 given Moment of Inertia
Go Radius 2 given Moment of Inertia = sqrt((Moment of Inertia-(Mass 1*Radius of Mass 1^2))/Mass 2)
Radius 1 given Moment of Inertia
Go Mass 2 of Diatomic Molecule = sqrt((Moment of Inertia-(Mass 2*Radius of Mass 2^2))/Mass 1)
Mass 2 given Moment of Inertia
Go Mass 2 given Moment of Inertia = (Moment of Inertia-(Mass 1*Radius of Mass 1^2))/Radius of Mass 2^2
Mass 1 given Moment of Inertia
Go Mass2 of object1 = (Moment of Inertia-(Mass 2*Radius of Mass 2^2))/Radius of Mass 1^2
Radius 1 given Rotational Frequency
Go Mass 2 of Diatomic Molecule = Velocity of Particle with Mass m1/(2*pi*Rotational Frequency)
Radius 1 of Rotation given Masses and Bond Length
Go Radius 1 of Rotation = Mass 2*Bond Length/(Mass 1+Mass 2)
Radius 2 of Rotation given Masses and Bond Length
Go Radius of Mass 2 = Mass 1*Bond Length/(Mass 1+Mass 2)
Radius 2 given Rotational Frequency
Go Radius of Mass 2 = Velocity of Particle with Mass m2/(2*pi*Rotational Frequency)
Reduced Mass
Go Reduced Mass = ((Mass 1*Mass 2)/(Mass 1+Mass 2))
Mass 1 of Diatomic Molecule
Go Mass 1 of Diatomic Molecule = Mass 2*Radius of Mass 2/Radius of Mass 1
Mass 2 of Diatomic Molecule
Go Mass 2 of Diatomic Molecule = Mass 1*Radius of Mass 1/Radius of Mass 2
Radius 2 of Rotation
Go Radius 1 given Rotational Frequency = Mass 1*Radius of Mass 1/Mass 2
Radius 1 of Rotation
Go Radius 1 of Rotation = Mass 2*Radius of Mass 2/Mass 1

Radius 1 of Rotation Formula

Radius 1 of Rotation = Mass 2*Radius of Mass 2/Mass 1
Rr1 = m2*R2/m1

How do we get Radius 1 of rotation?

System can be solved by using the concept of reduce mass which allows it to be treated as one rotating body. Center of mass (as frame of reference) is the point around which pure rotation can occur. In this case of diatomic, angular velocity is same for both atoms. Thus on equating angular momentum we get the required relation. Radius 1 of rotation can be calculated by using the concept of reduced mass, i.e.
M1 *R1 = M2 *R2
where M1 = Mass 1 of diatomic molecule; M2 =Mass 2 of diatomic molecule; R1 and R2 are respected distances from center of mass.

How to Calculate Radius 1 of Rotation?

Radius 1 of Rotation calculator uses Radius 1 of Rotation = Mass 2*Radius of Mass 2/Mass 1 to calculate the Radius 1 of Rotation, The Radius 1 of rotation is a distance of mass 1 of diatomic molecule such that it satisfies equilibrium conditions for rotation about center of mass (or point about which rotation occurs). Radius 1 of Rotation is denoted by Rr1 symbol.

How to calculate Radius 1 of Rotation using this online calculator? To use this online calculator for Radius 1 of Rotation, enter Mass 2 (m2), Radius of Mass 2 (R2) & Mass 1 (m1) and hit the calculate button. Here is how the Radius 1 of Rotation calculation can be explained with given input values -> 342.8571 = 16*0.03/14.

FAQ

What is Radius 1 of Rotation?
The Radius 1 of rotation is a distance of mass 1 of diatomic molecule such that it satisfies equilibrium conditions for rotation about center of mass (or point about which rotation occurs) and is represented as Rr1 = m2*R2/m1 or Radius 1 of Rotation = Mass 2*Radius of Mass 2/Mass 1. Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it, Radius of Mass 2 is a distance of mass 2 from the center of mass & Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it.
How to calculate Radius 1 of Rotation?
The Radius 1 of rotation is a distance of mass 1 of diatomic molecule such that it satisfies equilibrium conditions for rotation about center of mass (or point about which rotation occurs) is calculated using Radius 1 of Rotation = Mass 2*Radius of Mass 2/Mass 1. To calculate Radius 1 of Rotation, you need Mass 2 (m2), Radius of Mass 2 (R2) & Mass 1 (m1). With our tool, you need to enter the respective value for Mass 2, Radius of Mass 2 & Mass 1 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 Radius 1 of Rotation?
In this formula, Radius 1 of Rotation uses Mass 2, Radius of Mass 2 & Mass 1. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Radius 1 of Rotation = Mass 2*Bond Length/(Mass 1+Mass 2)
  • Radius 1 of Rotation = Mass 2*Bond Length/(Mass 1+Mass 2)
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