How to convert rev/s to rad/s?
Understand the Problem
The question asks for the method to convert rotational speed from revolutions per second (rev/s) to radians per second (rad/s). This involves knowing that one revolution is equal to 2π radians, allowing us to apply a simple conversion factor.
Answer
The formula to convert is $\text{Speed in rad/s} = \text{Speed in rev/s} \times 2\pi$.
Answer for screen readers
The conversion formula is $\text{Speed in rad/s} = \text{Speed in rev/s} \times 2\pi$.
Steps to Solve
- Identify the conversion factor
To convert revolutions per second to radians per second, we need to know how many radians are in one revolution. One revolution is equal to $2\pi$ radians.
- Set up the conversion
If we have a rotational speed of $x$ revolutions per second, we can express this in radians per second by multiplying by our conversion factor: $$ \text{Speed in rad/s} = \text{Speed in rev/s} \times 2\pi $$
- Perform the calculation
If $x$ is the speed in revolutions per second, then the speed in radians per second is: $$ \text{Speed in rad/s} = x \times 2\pi $$
- Example calculation
For instance, if the speed is $3$ rev/s, then: $$ \text{Speed in rad/s} = 3 \times 2\pi = 6\pi , \text{rad/s} $$
The conversion formula is $\text{Speed in rad/s} = \text{Speed in rev/s} \times 2\pi$.
More Information
For example, if an object rotates at a speed of 1 revolution per second, it spins through $2\pi$ radians every second. This is a common conversion used in physics and engineering when analyzing rotational motion.
Tips
- Forgetting the conversion factor: Ensure you remember that 1 revolution equals $2\pi$ radians.
- Mixing up units: Double-check that you're converting from rev/s to rad/s and not the other way around.
