Ch 12: Rotation of a Rigid Body

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 12: Rotation of a Rigid Body

문제 33c

12장, 문제 33c

A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. What is the speed of a point at the bottom edge of the tire?

검증된 단계별 안내

Step 1: Understand the problem. The speed of a point at the bottom edge of the tire is influenced by both the translational motion of the car and the rotational motion of the tire. At the bottom edge, the rotational velocity of the tire opposes the translational velocity of the car.

Step 2: Recall the relationship between linear velocity and angular velocity. The linear velocity of a point on the edge of a rotating object is given by the formula:

v = r ω

, where

r

is the radius of the tire and

ω

is the angular velocity.

Step 3: Calculate the radius of the tire. The diameter is given as 60 cm, so the radius is half of that:

r = \frac{60}{2} = 30

cm or

0.3

Step 4: Determine the angular velocity of the tire. The car's translational speed is related to the tire's angular velocity by the formula:

v = r ω

. Rearrange to solve for

ω

ω = \frac{v}{r}

. Substitute

v = 20

m/s and

r = 0.3

m to find

ω

Step 5: Combine the translational and rotational velocities. At the bottom edge of the tire, the rotational velocity opposes the translational velocity. The total speed of the point at the bottom edge is given by:

v = v translational - v rotational

. Substitute the values to find the result.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Linear Speed

Linear speed refers to the distance traveled per unit of time by an object moving along a path. In this context, the car's speed of 20 m/s indicates how fast the entire vehicle is moving forward. Understanding linear speed is crucial for analyzing the motion of points on the tire, as it helps relate the speed of the car to the rotational motion of the tire.

Rotational Motion

Rotational motion describes the movement of an object around a central axis. For a tire, this involves the rotation about its center as it rolls. The relationship between linear speed and rotational speed is essential for determining how fast a point on the tire's edge moves, as the tire's rotation affects the speed of points on its circumference.

Point of Contact Speed

The speed of a point at the bottom edge of the tire, also known as the point of contact, is influenced by both the linear speed of the car and the rotational motion of the tire. When the tire rolls without slipping, the point of contact momentarily has a speed of zero relative to the ground. Thus, to find the speed of this point, one must consider the combination of the tire's rotation and the car's forward motion.