How to Graph Moment of Inertia and Frictional Torque?

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To graph the moment of inertia (I) and frictional torque from the equation rm(g-a) = I(a/r) + Frictional Torque, the variables can be rearranged to fit the linear equation format y = mx + b. In this case, I can be represented as the slope (m), while the frictional torque serves as the y-intercept (b). The variables m (mass) and a (acceleration) can be used as the x and y variables, respectively. By plotting acceleration against the rearranged equation, the slope will yield the moment of inertia, and the intercept will provide the frictional torque. This approach allows for a clear graphical representation of both physical quantities.
cam borrett
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Homework Statement



The moment of inertia (I) of the bicycle wheel about the axle, can be obtained graphically using the equation:
rm(g-a) = I(a/r)+Frictional Torque. Explain how to form two variables so that, I and Frictional Torque can be obtained from a linear graph. Identify the constants corresponding to the slope and intercept of the proposed linear graph.

r = 0.018m
m=0.200kg
g=9.8m/s^2
a=0.002812
I=?
Frictional Torque= ?

Homework Equations



(1) rm(g-a) = I(a/r)+Frictional Torque.

(2) y=mx+b

3. The Attempt at a Solution

Im not sure if I am 100% right on this but, equation one could take the form of equation two.
m being I.
x being what's changing, ie. acceleration
b being the y intercept, ie frictional torque

Just unsure where to go from there a how to graph it.
 
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cam borrett said:
rm(g-a) = I(a/r)+Frictional Torque.
Presumably these variable relate to a physical set-up of some kind. Please describe it.
 
The two variables are m and a. Try and rewrite the equation so that they become the x and y variables in the linear equation (or a combination of the variables!). The frictional torque and moment of inertia should then part of gradient and y-intercept values (r and g will also appear in these).
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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