Ch 10: Dynamics of Rotational Motion

Young & Freedman Calc - University Physics 14th Edition

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

Young & Freedman Calc 14th Edition

Ch 10: Dynamics of Rotational Motion

문제 28b

10장, 문제 28b

A bicycle racer is going downhill at 11.0 m/s when, to his horror, one of his 2.25-kg wheels comes off as he is 75.0 m above the foot of the hill. We can model the wheel as a thin-walled cylinder 85.0 cm in diameter and ignore the small mass of the spokes. How much total kinetic energy does the wheel have when it reaches the bottom of the hill?

검증된 단계별 안내

First, identify the types of energy involved. The wheel has both translational kinetic energy due to its linear motion and rotational kinetic energy due to its spinning.

Calculate the initial potential energy of the wheel at the top of the hill using the formula:

E = m g h

, where

m

is the mass of the wheel,

g

is the acceleration due to gravity, and

h

is the height above the foot of the hill.

Determine the translational kinetic energy using the formula:

E = \frac{1}{2} m v^{2}

, where

v

is the linear velocity of the wheel.

Calculate the rotational kinetic energy using the formula:

E = \frac{1}{2} I ω^{2}

, where

I

is the moment of inertia of the wheel and

ω

is the angular velocity. For a thin-walled cylinder,

I

can be calculated as

I = m r^{2}

, where

r

is the radius of the wheel.

Sum the translational and rotational kinetic energies to find the total kinetic energy of the wheel when it reaches the bottom of the hill.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

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

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v^2, where m is mass and v is velocity. In this scenario, the wheel's kinetic energy includes both translational and rotational components as it rolls downhill.

Rotational Kinetic Energy

Rotational kinetic energy is the energy due to an object's rotation, given by KE_rot = 0.5 * I * ω^2, where I is the moment of inertia and ω is the angular velocity. For a thin-walled cylinder, I = m * r^2, where r is the radius, which is crucial for calculating the wheel's energy as it rolls.

Conservation of Energy

The conservation of energy principle states that energy cannot be created or destroyed, only transformed. As the wheel descends, its potential energy converts into kinetic energy, allowing us to calculate the total kinetic energy at the bottom by considering both translational and rotational forms.