Ch 09: Rotation of Rigid Bodies

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 09: Rotation of Rigid Bodies

문제 24c

9장, 문제 24c

An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s². What is the tangential speed of a point on the rim of the turntable at t = 0.200 s?

검증된 단계별 안내

Convert the given angular velocity and angular acceleration from revolutions per second (rev/s) and revolutions per second squared (rev/s²) to radians per second (rad/s) and radians per second squared (rad/s²), respectively. Use the conversion factor: 1 revolution = 2π radians.

Calculate the angular velocity (ω) at time t = 0.200 s using the formula for angular velocity under constant angular acceleration:

ω = ω o + α t

, where

ω o

is the initial angular velocity,

α

is the angular acceleration, and

t

is the time.

Determine the radius of the turntable from its diameter. The radius is half the diameter:

r = \frac{0.750}{2} = 0.375 m

Use the relationship between tangential speed (v) and angular velocity (ω):

v = r ω

, where

r

is the radius and

ω

is the angular velocity at t = 0.200 s.

Substitute the values of

r

and

ω

into the formula for tangential speed to find the result:

v = 0.375 \cdot ω

비슷한 문제에 대한 검증된 영상 답변:

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 Velocity

Angular velocity is a measure of how quickly an object rotates around an axis, expressed in radians per second or revolutions per second. In this scenario, the initial angular velocity of the turntable is given as 0.250 rev/s, indicating the rate of rotation at the start of the observation.

Angular Acceleration

Angular acceleration refers to the rate of change of angular velocity over time, typically measured in revolutions per second squared. In this case, the turntable has a constant angular acceleration of 0.900 rev/s², which means its rotational speed increases steadily as time progresses.

Tangential Speed

Tangential speed is the linear speed of a point on the circumference of a rotating object, calculated as the product of the angular velocity and the radius of the rotation. For the turntable, the tangential speed at any moment can be determined using the formula v = r * ω, where r is the radius and ω is the angular velocity at that time.