Solve each problem. See Example 6. Rotating Airplane Propeller An airplane propeller rotates 1000 times per min. Find the number of degrees that a point on the edge of the propeller will rotate in 2 sec.

Verified step by step guidance

1. Identify the given information: the propeller rotates 1000 times per minute, and we want to find the degrees rotated in 2 seconds.
2. Convert the rotation rate from revolutions per minute to revolutions per second by dividing 1000 by 60, since there are 60 seconds in a minute. This gives revolutions per second.
3. Calculate the total number of revolutions in 2 seconds by multiplying the revolutions per second by 2.
4. Recall that one full revolution corresponds to 360 degrees. Use this to convert the total revolutions into degrees by multiplying the number of revolutions by 360.
5. Write the final expression for the degrees rotated in 2 seconds as: \(\text{Degrees} = \left(\frac{1000}{60} \times 2\right) \times 360\).

Key Concepts

Angular Velocity

Angular velocity measures how fast an object rotates, typically expressed in revolutions per minute (rpm) or radians per second. It indicates the angle covered per unit time, which is essential for converting rotational speed into degrees or radians over a given time interval.

Unit Conversion Between Time and Angle

To solve rotation problems, it's crucial to convert time units (minutes to seconds) and angular units (revolutions to degrees). Since one revolution equals 360 degrees, multiplying the number of revolutions by 360 gives the total degrees rotated.

Proportional Reasoning in Rotation

Proportional reasoning helps relate the rotation in a given time to the total rotation rate. By setting up ratios between time intervals and revolutions, one can find the degrees rotated in any specified duration, such as 2 seconds in this problem.