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Ch 09: Rotation of Rigid Bodies
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Young & Freedman Calc 14th EditionCh 09: Rotation of Rigid Bodies문제 20a
9장, 문제 20a

A compact disc (CD) stores music in a coded pattern of tiny pits 10-7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track?

검증된 단계별 안내
1
Step 1: Understand the relationship between linear speed and angular speed. The formula to relate linear speed (v) and angular speed (ω) is: v = ω * r, where r is the radius of the circular path. Rearrange this formula to solve for angular speed: ω = v / r.
Step 2: Convert the given radii from millimeters to meters. The inner radius is 25.0 mm, which is 0.025 m, and the outer radius is 58.0 mm, which is 0.058 m.
Step 3: Use the formula ω = v / r to calculate the angular speed at the innermost part of the track. Substitute the given linear speed (v = 1.25 m/s) and the inner radius (r = 0.025 m) into the formula.
Step 4: Similarly, use the same formula ω = v / r to calculate the angular speed at the outermost part of the track. Substitute the given linear speed (v = 1.25 m/s) and the outer radius (r = 0.058 m) into the formula.
Step 5: Compare the angular speeds at the inner and outer radii. Note that the angular speed decreases as the radius increases, since the linear speed is constant.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념

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

Angular Speed

Angular speed is a measure of how quickly an object rotates around a central point, typically expressed in radians per second. It is calculated by the formula ω = v/r, where ω is the angular speed, v is the linear speed, and r is the radius from the center of rotation. In the context of a CD, as the disc spins, different points on the disc have varying distances from the center, affecting their angular speeds.
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가이드 코스
07:59
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Linear Speed

Linear speed refers to the distance traveled per unit of time along a path. In the case of a compact disc, the linear speed is constant at 1.25 m/s, meaning that any point on the disc moves at this speed as the disc rotates. This constant linear speed is crucial for determining the angular speed at different radii of the disc.
추천 영상:
가이드 코스
07:31
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Radius of Rotation

The radius of rotation is the distance from the center of rotation to the point of interest on the rotating object. For a compact disc, the inner radius is 25.0 mm and the outer radius is 58.0 mm. The radius directly influences the angular speed; as the radius increases, the angular speed decreases for a constant linear speed, illustrating the inverse relationship between these two quantities.
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가이드 코스
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관련 실천
교과서 질문

CA compact disc (CD) stores music in a coded pattern of tiny pits 10-7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line?

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교과서 질문

An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.00 s. Find the angular acceleration in rev/s2 and the number of revolutions made by the motor in the 4.00-s interval.

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교과서 질문

A compact disc (CD) stores music in a coded pattern of tiny pits 10-7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. What is the average angular acceleration of a maximum duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.

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교과서 질문

A wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s2. Compute the radial acceleration of a point on the rim for the instant the wheel completes its second revolution from the relationship arad = ω2r.

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교과서 질문

A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 cm. The power is off for 30.0 s, and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 200 complete revolutions. At what rate is the flywheel spinning when the power comes back on?

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교과서 질문

An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.00 s. How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in part (a)?

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