A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door's moment of inertia for rotation on its hinges?

검증된 단계별 안내

Step 1: Understand the problem. The moment of inertia (I) is a measure of an object's resistance to rotational motion about a specific axis. For this problem, the door is treated as a rectangular object rotating about one of its edges (the hinges). The formula for the moment of inertia of a rectangular object about an edge parallel to one of its sides is:

I = \frac{1}{3} m w^{2}

, where m is the mass and w is the width of the door.

Step 2: Convert the dimensions of the door into meters, as SI units are required for consistency. The width of the door is given as 91 cm, which is equivalent to 0.91 m. The height of the door (220 cm) is not relevant for this calculation since the rotation is about the hinges along the height.

Step 3: Substitute the given values into the formula. The mass of the door (m) is 25 kg, and the width (w) is 0.91 m. The formula becomes:

I = \frac{1}{3} (25) ({0.91}^{2})

Step 4: Simplify the expression by squaring the width (0.91 m) and multiplying it by the mass (25 kg). Then, multiply the result by 1/3 to find the moment of inertia.

Step 5: The final result will give the moment of inertia of the door for rotation about its hinges. Ensure the units are in kg·m², as this is the standard unit for moment of inertia.

비슷한 문제에 대한 검증된 영상 답변:

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.

Moment of Inertia

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution relative to the axis of rotation. For a solid rectangular object, the moment of inertia can be calculated using specific formulas that take into account its dimensions and mass.

Axis of Rotation

The axis of rotation is the line about which an object rotates. In the case of a door, the axis is typically at the hinges. The position of this axis significantly affects the moment of inertia, as the distribution of mass relative to the axis determines how easily the object can be rotated.

A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door's moment of inertia for rotation on its hinges?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Moment of Inertia

Axis of Rotation

Parallel Axis Theorem