Find inner radius of hollow cylinder given inertia

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SUMMARY

The discussion centers on calculating the inner radius (R1) of a hollow cylinder, specifically a roll of toilet paper with an outer radius (R2) of 7.0 cm, mass (M) of 320 g, and moment of inertia (I) of 6.0 x 10-4 kg m2. The moment of inertia formula for a hollow cylinder, I = 1/2 M (R12 + R22), was applied, but the user encountered a negative value when attempting to solve for R1, indicating a potential error in the provided moment of inertia value. The user plans to verify the moment of inertia with the professor to proceed with the problem.

PREREQUISITES
  • Understanding of the moment of inertia for hollow cylinders
  • Ability to convert units to SI units
  • Familiarity with algebraic manipulation of equations
  • Basic knowledge of rotational dynamics
NEXT STEPS
  • Verify the moment of inertia value with the professor
  • Review the derivation of the moment of inertia formula for hollow cylinders
  • Practice solving similar problems involving rotational motion
  • Explore the implications of negative values in physical calculations
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Students studying physics, particularly those focusing on rotational dynamics and moment of inertia calculations, as well as educators seeking to clarify concepts related to hollow cylinders.

alem
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Homework Statement


A roll of toilet paper ( a partially hollow cylinder with R2=7.0 cm, M=320 g, I=6.0x 10 ^(-4) kg m is mounted on an axle. initially at rest, until a child grabs the end and starts running at a constant linear acceleration.

part a) what is the inner radius (R1)

Homework Equations



I know the equation for a hollow cylinder's moment of inertia is I=1/2 M (R1^2 + R2^2)

The Attempt at a Solution



I converted all my units to S.I. units

7 cm= 0.07m
320g= 0.320kg

I rearranged the equation as
R= ({(2*I)/M} -R2^2) ^(1/2)
2 (6.0x 10^-4)=0.0012 kg m
0.0012 kg m/.320 kg= .00375m
0.00375 m-(0.07m)^2= -0.0015 m^2
I would now need to take the square-root of this number, but its a negative number. I cannot seem to find what I did wrong. and I need part a) to find the other four parts of this question. Thanks to anyone who takes the time to help.

Homework Statement


Homework Equations


The Attempt at a Solution

 
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There is likely an error in the given value of I = 1.6*10^-4 kg.m^2. Bummer. Did you copy it down correctly?
 
its straight out of the worksheet. Thanks though. I will email the professor
 

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