Find inner radius of hollow cylinder given inertia

AI Thread Summary
The discussion revolves around calculating the inner radius (R1) of a hollow cylinder given its moment of inertia (I), mass (M), and outer radius (R2). The participant has converted the values to SI units and attempted to rearrange the moment of inertia formula but encountered a negative value when calculating R1, indicating a potential error. Another contributor suggests that the moment of inertia value provided may be incorrect, prompting the original poster to consider contacting the professor for clarification. The resolution of this issue is crucial for solving the remaining parts of the problem. Accurate values are essential for correct calculations in physics problems involving rotational dynamics.
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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
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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