Convert rotation to second of arc

Learn how to convert 1 rotation to second of arc step by step.

Calculation Breakdown

Set up the equation

1.0 (r o t a t i o n) = x (s e c o n d o f a r c)

Define the base values of the selected units in relation to the SI unit

(r a d i a n)

Left side: 1.0 (r o t a t i o n) = 2.0 \times π (r a d i a n) = 2.0 \times π (r a d)

Right side: 1.0 (s e c o n d o f a r c) = \frac{π}{6.48 \times 10^{5}} (r a d i a n) = \frac{π}{6.48 \times 10^{5}} (r a d)

Insert known values into the conversion equation to determine

x

1.0 (r o t a t i o n) = x (s e c o n d o f a r c)

Insert known values =>

1.0 \times 2.0 \times π \times (r a d i a n) = x \times \frac{π}{6.48 \times 10^{5}} \times (r a d i a n)

Or

1.0 \cdot 2.0 \times π \cdot (r a d) = x \cdot \frac{π}{6.48 \times 10^{5}} \cdot (r a d)

Cancel SI units

1.0 \times 2.0 \times π \cdot (r a d) = x \times \frac{π}{6.48 \times 10^{5}} \times (r a d)

Conversion Equation

2.0 \times π = x \times \frac{π}{6.48 \times 10^{5}}

Cancel factors on both sides

Cancel factors

π \times 2.0 = x \times \frac{π}{6.48 \times 10^{5}}

Simplify

2.0 = x \times \frac{1.0}{6.48 \times 10^{5}}

Switch sides

x \times \frac{1.0}{6.48 \times 10^{5}} = 2.0

Isolate

x

Multiply both sides by

(\frac{6.48 \times 10^{5}}{1.0})

x \times \frac{1.0}{6.48 \times 10^{5}} \times \frac{6.48 \times 10^{5}}{1.0} = 2.0 \times \frac{6.48 \times 10^{5}}{1.0}

Cancel

x \times \frac{1.0 \times 6.48 \times 10^{5}}{6.48 \times 10^{5} \times 1.0} = 2.0 \times \frac{6.48 \times 10^{5}}{1.0}

Simplify

x = 2.0 \times 6.48 \times 10^{5}

Solve

x

x = 1296000 = 1.296 \times 10^{6}

Conversion Equation

1.0 (r o t a t i o n) = 1.296 \times 10^{6} (s e c o n d o f a r c)

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