Have you ever come across a situation where you need to convert a rotational speed from revolutions per minute (RPM) to radians per second (rad/s)? Understanding how to make this conversion is crucial, especially in fields like physics and engineering where rotational motion is common. In this article, we will explain the step-by-step process to convert from RPM to rad/s.

To begin, let’s understand the fundamental concepts involved in this conversion. RPM measures the number of full rotations an object makes in one minute, while rad/s measures the angular velocity of an object in radians covered per second. Radians are a unit of measurement for angles.

To convert from RPM to rad/s, we need to take into account the relationship between rotational speed and time. One complete revolution is equal to 2π radians. Therefore, to convert RPM to rad/s, we can use the following formula:

Angular velocity (in rad/s) = RPM × 2π/60

Now, let’s break down the steps to convert RPM to rad/s:

Step 1: Identify the given value in RPM. For example, let’s assume we have a rotational speed of 100 RPM.

Step 2: Apply the conversion formula. Angular velocity (in rad/s) = 100 RPM × 2π/60. Simplifying the equation further, we get angular velocity = 100 × 2π/60.

Step 3: Calculate the value using a calculator or by hand. Angular velocity = 100 × 2π/60 ≈ 10.47198 rad/s.

Step 4: Round the final answer to an appropriate number of significant figures. In this case, let’s round it to five decimal places: 10.47198 rad/s.

Therefore, if you have a rotational speed of 100 RPM, its equivalent in radians per second is approximately 10.47198 rad/s.

It is worth noting that the conversion factor used in the formula, 2π/60, is derived from the fact that there are 2π radians in one complete revolution (360 degrees) and 60 seconds in one minute. By multiplying the rotational speed in RPM by this conversion factor, we effectively cancel out the units of minutes and revolutions, leaving us with rad/s, which is the desired unit.

In conclusion, converting from RPM to rad/s involves multiplying the rotational speed by 2π/60. This conversion is important in various fields, including physics and engineering, where accurate measurements of angular velocity are required. Understanding this conversion process enables you to easily work with rotational speed in both RPM and rad/s, ensuring you can perform calculations and solve problems involving rotational motion confidently.

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