Find the angular speed ω for each of the following.

a wind turbine with blades turning at a rate of 15 revolutions per minute

검증된 단계별 안내

Understand that angular speed \( \omega \) is the rate of change of the angle with respect to time, usually measured in radians per second (rad/s).

Note that the problem gives the rotational speed in revolutions per minute (rpm), so the first step is to convert revolutions to radians. Recall that one revolution corresponds to \( 2\pi \) radians.

Convert the given speed from revolutions per minute to radians per minute by multiplying the number of revolutions by \( 2\pi \): \[ \omega = 15 \times 2\pi \quad \text{radians per minute} \]

Next, convert the angular speed from radians per minute to radians per second by dividing by 60 (since there are 60 seconds in a minute): \[ \omega = \frac{15 \times 2\pi}{60} \quad \text{radians per second} \]

This expression now represents the angular speed \( \omega \) in radians per second. You can simplify this expression further if needed.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Angular Speed (ω)

Angular speed measures how fast an object rotates or revolves relative to a fixed point, expressed in radians per second or revolutions per minute. It quantifies the rate of change of the angular position of a rotating body.

Conversion between Revolutions and Radians

One complete revolution corresponds to 2π radians. To convert angular speed from revolutions per minute (rpm) to radians per second, multiply by 2π and divide by 60, since there are 60 seconds in a minute.

Units and Dimensional Analysis

Understanding and converting units correctly is essential in trigonometry and physics problems. Here, converting rpm to radians per second ensures the angular speed is in standard SI units, facilitating further calculations or comparisons.

Find the angular speed ω for each of the following.a wind turbine with blades turning at a rate of 15 revolutions per minute