AP Physics 1 textbook flaw?

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1. Apr 30, 2017

Ercillent

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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)

Last edited: Apr 30, 2017
2. Apr 30, 2017

kuruman

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

3. Apr 30, 2017

Ercillent

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

4. Apr 30, 2017

Staff: Mentor

The answer in the book is correct.
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

5. Apr 30, 2017

Ercillent

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

6. Apr 30, 2017

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, Krot=(1/2)I w2.