Is the AP Physics 1 textbook flawed in its explanation of moment of inertia?

[Ercillent]

Homework Statement

[/B]
I'm probably missing something basic here but:

The moment of inertia of a body does NOT depend on which of the following? (choose 2 answers)

A: The angular acceleration of the body
B. The distribution of mass in the body
C. The angular velocity of the body
D. The axis of rotation of the body
E. The mass of the body

Homework Equations

L = Iw² where L = angular momentum, I = inertia and w = angular velocity

The Attempt at a Solution

If L = Iw² > > >(rearranged) >>> I = L/w². How does Inertia not depend on angular velocity if the variable for angular vel (w) is in the equation? The answers in the back of the book say (A) and (C)

 

[kuruman]

Does mass depend on speed because KE = (1/2)mv²?

 

[Ercillent]

Does mass depend on speed because KE = (1/2)mv²?

But doesn't inertia depend on angular speed if I = L/w²

 

[berkeman]

If L = Iw2 > > >(rearranged) >>> I = L/w2. How does Inertia not depend on angular velocity if the variable for angular vel (w) is in the equation? The answers in the back of the book say (A) and (C)

The answer in the book is correct.

But doesn't inertia depend on angular speed if I = L/w²

Not for a rigid body. The only way the moment of inertia depends on angular velocity is if you have a non-rigid structure like a mechanical governor. As kuruman suggests, just because you can rearrange an equation to put an independent variable on one side of the equation, does not transform it into a dependent variable. Are you familiar with those terms?

http://4.bp.blogspot.com/-SxXjZFy_Lgk/Th6KS2nfPdI/AAAAAAAAACY/oeGWJmL6rsc/s1600/governor.gif

 

[Ercillent]

Oh gotcha. Yeah you're right that wouldn't make any sense. Thanks!

 

[kuruman]

As a postscript and to keep the thread correct for future viewers, the equation L = I w² is not valid. If L is angular momentum and w is angular speed, then L = I w. If w² is to be kept, then we are talking rotational energy, K_rot=(1/2)I w².