Revolutions per minute (RPM) is a unit of rotational speed that indicates the number of full rotations completed by an object around a fixed axis in one minute. It's commonly used to measure the rotational speed of mechanical components, such as engines, motors, and other rotating equipment.

Applications of RPM:

• Automobiles: RPM is used to measure the speed at which an engine's crankshaft is rotating. Higher RPMs generally indicate a higher engine speed.
• Machinery: In industrial settings, RPM is used to monitor the speed of equipment like drills, lathes, and conveyors to ensure they are operating within safe and efficient limits.
• CD/DVD Players: The RPM indicates how fast the disc is spinning, which can affect data read/write speeds.

Conversion:

• To radians per second (rad/s): Since there are $2\pi$ radians in a full rotation and 60 seconds in a minute, you can convert RPM to rad/s using the formula:

  $$\text{rad/s} = \text{RPM} \times \frac{2\pi}{60}$$

• To hertz (Hz): Hertz is the unit of frequency, and 1 Hz equals 1 rotation per second. You can convert RPM to Hz using the formula:

  $$\text{Hz} = \frac{\text{RPM}}{60}$$

Understanding RPM is crucial in various fields to ensure that devices are functioning properly and efficiently.