A 2.00-kg rock has a horizontal velocity of magnitude 12.0 m/s when it is at point P in Fig. E10.35. At this instant, what are the magnitude and direction of its angular momentum relative to point O?

검증된 단계별 안내

Identify the given values: mass of the rock (m) is 2.00 kg, velocity (v) is 12.0 m/s, distance from point O to point P (r) is 8.00 m, and the angle between the line OP and the horizontal is 36.9 degrees.

Recall the formula for angular momentum (L) relative to a point: L = r * m * v * sin(θ), where θ is the angle between the position vector and the velocity vector.

Determine the angle θ between the position vector and the velocity vector. Since the velocity is horizontal and the position vector makes an angle of 36.9 degrees with the horizontal, θ = 90 degrees - 36.9 degrees.

Substitute the known values into the angular momentum formula: L = 8.00 m * 2.00 kg * 12.0 m/s * sin(53.1 degrees).

Calculate the sine of 53.1 degrees and multiply all the values to find the magnitude of the angular momentum. The direction of the angular momentum is perpendicular to the plane formed by the position vector and the velocity vector, following the right-hand rule.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

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주요 개념

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

Angular Momentum

Angular momentum is a measure of the rotational motion of an object and is given by the cross product of the position vector and the linear momentum vector. For a point mass, it is calculated as L = r × p, where r is the position vector from the point of rotation to the object, and p is the linear momentum (mass times velocity).

Cross Product

The cross product is a vector operation used to find a vector perpendicular to two given vectors in three-dimensional space. It is essential in calculating angular momentum, as it determines the direction of the angular momentum vector. The magnitude of the cross product is given by |A × B| = |A||B|sin(θ), where θ is the angle between vectors A and B.

Conservation of Angular Momentum

The conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of the system remains constant. This principle is crucial in analyzing systems where rotational motion is involved, as it allows for the prediction of future states of the system based on initial conditions.