The propeller of a 90-horsepower outboard motor at full throttle rotates at exactly 5000 revolutions per min. Find the angular speed of the propeller in radians per second.

Verified step by step guidance

1. Start by identifying the given information: the propeller rotates at 5000 revolutions per minute.
2. Convert revolutions per minute to revolutions per second by dividing 5000 by 60, since there are 60 seconds in a minute.
3. Recall that one complete revolution is equal to $2\pi$ radians.
4. Multiply the number of revolutions per second by $2\pi$ to convert to radians per second.
5. The result from the previous step gives the angular speed of the propeller in radians per second.

Key Concepts

Angular Speed

Angular speed is a measure of how quickly an object rotates around a central point, typically expressed in radians per second. It quantifies the angle through which an object rotates in a given time period. To convert from revolutions per minute (RPM) to radians per second, one can use the conversion factor that 1 revolution equals 2π radians.

Conversion of Units

Unit conversion is essential in physics and engineering to ensure that measurements are expressed in compatible units. In this case, converting revolutions per minute to radians per second involves multiplying the RPM value by a conversion factor that accounts for the number of seconds in a minute and the radians in a revolution. This process allows for accurate calculations in different unit systems.

Revolutions to Radians

Understanding the relationship between revolutions and radians is crucial in trigonometry. One complete revolution corresponds to 2π radians. This relationship is foundational for converting angular measurements and is frequently used in problems involving circular motion, such as calculating the angular speed of rotating objects.