Solve each problem. Rotating Pulley A pulley is rotating 320 times per min. Through how many degrees does a point on the edge of the pulley move in 2/3 sec?

검증된 단계별 안내

Identify the given information: the pulley rotates 320 times per minute, and we want to find the degrees moved in \( \frac{2}{3} \) seconds.

Convert the rotation rate from revolutions per minute (rpm) to revolutions per second (rps) by dividing 320 by 60, since there are 60 seconds in a minute: \( \text{rps} = \frac{320}{60} \).

Calculate the number of revolutions the pulley makes in \( \frac{2}{3} \) seconds by multiplying the revolutions per second by \( \frac{2}{3} \): \( \text{revolutions} = \text{rps} \times \frac{2}{3} \).

Recall that one full revolution corresponds to 360 degrees. To find the total degrees moved, multiply the number of revolutions by 360: \( \text{degrees} = \text{revolutions} \times 360 \).

Combine all the steps into one expression if desired, but do not calculate the final numeric value as per instructions.

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주요 개념

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

Angular Displacement

Angular displacement measures the angle through which a point or line has been rotated in a specified direction. It is usually expressed in degrees or radians and represents the change in angular position of a rotating object.

Conversion between Rotations and Degrees

One complete rotation corresponds to 360 degrees. To find the angular displacement in degrees, multiply the number of rotations by 360. This conversion is essential when relating rotational speed to angular displacement.

Relating Rotational Speed to Time

Rotational speed given in rotations per minute (rpm) can be converted to rotations per second by dividing by 60. Multiplying this by the time interval in seconds gives the total rotations during that time, which can then be converted to angular displacement.