Suggested languages for you:

Americas

Europe

39 P

Expert-verifiedFound in: Page 335

Book edition
9th Edition

Author(s)
Raymond A. Serway, John W. Jewett

Pages
1624 pages

ISBN
9781133947271

**Question: A uniform, thin, solid door has height 2.20 m, width 0.870 m, and mass 23.0 kg. (a) Find its moment of inertia for rotation on its hinges. (b) Is any piece of data unnecessary?**

(a)The moment of inertia for rotation on its hinges is $I=5.8\u200a\text{kg}\xb7{\text{m}}^{2}$

(b)The piece of unnecessary data is height.

Moment of inertia about a given axis of rotation resists a change in its rotational motion; it can be regarded as a measure of rotational inertia of the body.

$I=\frac{L}{\omega}$

Given:

$M=23\text{kg}$

L (width of the floor)$=0.87\text{m}$

H (height of door) $=2.2\text{m}$

(a)

The door can be modeled as long, thin rod with rotation axis through end, $I=\frac{1}{3}M{L}^{2}$.

Substituting the numerical values, we get

$\begin{array}{rcl}I& =& \frac{1}{3}\left(23\right)(0.87{)}^{2}\\ & =& 5.8\u200a\text{kg}\xb7{\text{m}}^{2}\end{array}$

So, the answer is $5.8\u200a\text{kg}\xb7{\text{m}}^{2}$.

(b)

The height of the door is the unnecessary piece of data.

So, the answer is height of the door.

94% of StudySmarter users get better grades.

Sign up for free