degrees per second to radians per second conversion

How to convert degrees per second to radians per second?

Degrees per second (°/s) is a unit that measures angular velocity, representing the angle turned through each second. To convert degrees per second to radians per second (rad/s), you need to use the fact that there are $2\pi$ radians in a full circle (360 degrees).

Here’s the conversion factor:

$1 \text{ degree} = \frac{\pi}{180} \text{ radians}$

So to convert from degrees per second to radians per second, you multiply by $\frac{\pi}{180}$:

$1 \text{ °/s} = 1 \times \frac{\pi}{180} \text{ rad/s} \approx 0.0174533 \text{ rad/s}$

Real-World Examples of Degrees per Second

1. Earth's Rotation:

   • The Earth rotates approximately 360 degrees in about 24 hours. Converting this to degrees per second: $\frac{360 \text{ degrees}}{24 \text{ hours} \times 3600 \text{ seconds/hour}} \approx 0.00417 \text{ °/s}$
   • In radians per second: $0.00417 \times \frac{\pi}{180} \approx 7.27 \times 10^{-5} \text{ rad/s}$

2. Rotating Kitchen Blender Blade:

   • Assume a kitchen blender blade spins at 6000 revolutions per minute (RPM). First, convert RPM to degrees per second: $6000 \text{ RPM} \times \frac{360 \text{ degrees}}{1 \text{ revolution}} \times \frac{1 \text{ minute}}{60 \text{ seconds}} = 36000 \text{ °/s}$
   • In radians per second: $36000 \times \frac{\pi}{180} \approx 628.32 \text{ rad/s}$

3. Ferris Wheel Rotation:

   • A Ferris wheel makes 1 revolution every 2 minutes. First, convert revolutions per minute to degrees per second: $\frac{1 \text{ revolution}}{2 \text{ minutes}} \times \frac{360 \text{ degrees}}{1 \text{ revolution}} \times \frac{1 \text{ minute}}{60 \text{ seconds}} = 3 \text{ °/s}$
   • In radians per second: $3 \times \frac{\pi}{180} \approx 0.05236 \text{ rad/s}$

By understanding and converting between these units, you can more accurately describe and compare rotational speeds in various contexts.