# Convert cycle / hour to radian / minute

Learn how to convert 1 cycle / hour to radian / minute step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{cycle}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{cycle}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{radian}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{rad}{s}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{radian}{minute}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{radian}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{rad}{s}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{cycle}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{π}{1.8 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} = \dfrac{π}{1.8 \times 10^{3}}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{60.0}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} \times \dfrac{60.0}{1.0} = \dfrac{π}{1.8 \times 10^{3}} \times \dfrac{60.0}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{60.0}}}{{\color{rgb(99,194,222)} \cancel{60.0}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{π \times 60.0}{1.8 \times 10^{3} \times 1.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{π \times 60.0}{1.8 \times 10^{3}}$$
Rewrite equation
$$\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times π \times 60.0}{1.8}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.1047197551\approx1.0472 \times 10^{-1}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{cycle}{hour}\right)\approx{\color{rgb(20,165,174)} 1.0472 \times 10^{-1}}\left(\dfrac{radian}{minute}\right)$$
The text passage provides a detailed step-by-step conversion of 1 cycle per hour to radians per minute, including the setup of the equation, the definition of base values, and the final calculation.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Convert cycle / hour to radian / minute

Learn how to convert 1 cycle / hour to radian / minute step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{cycle}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{cycle}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{radian}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{rad}{s}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{radian}{minute}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{radian}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{rad}{s}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{cycle}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{π}{1.8 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} = \dfrac{π}{1.8 \times 10^{3}}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{60.0}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} \times \dfrac{60.0}{1.0} = \dfrac{π}{1.8 \times 10^{3}} \times \dfrac{60.0}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{60.0}}}{{\color{rgb(99,194,222)} \cancel{60.0}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{π \times 60.0}{1.8 \times 10^{3} \times 1.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{π \times 60.0}{1.8 \times 10^{3}}$$
Rewrite equation
$$\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times π \times 60.0}{1.8}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.1047197551\approx1.0472 \times 10^{-1}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{cycle}{hour}\right)\approx{\color{rgb(20,165,174)} 1.0472 \times 10^{-1}}\left(\dfrac{radian}{minute}\right)$$
user
The text passage provides a detailed step-by-step conversion of 1 cycle per hour to radians per minute, including the setup of the equation, the definition of base values, and the final calculation.

TYPE: SINGLE_QUESTION_WITH_ANSWER